Yes. Memory does belong to the intellectual part of the soul because whoever has habitual knowledge is in potentiality to actual consideration.
Memoria pertinet ad partem animae intellectivam quia sciens in habitu est in potentia ad considerandum in actu.
The intelligible species is sometimes in the intellect only in potentiality, and then the intellect is said to be in potentiality. Sometimes the intelligible species is in the intellect as regards the ultimate completion of the act, and then it understands in act. And sometimes the intelligible species is in a middle state, between potentiality and act: and then we have habitual knowledge. In this way the intellect retains the species, even when it does not understand in act.
Species intelligibilis aliquando est in intellectu in potentia tantum, et tunc dicitur intellectus esse in potentia. Aliquando autem secundum ultimam completionem actus, et tunc intelligit actu. Aliquando medio modo se habet inter potentiam et actum, et tunc dicitur esse intellectus in habitu. Et secundum hunc modum intellectus conservat species, etiam quando actu non intelligit.
Memory, if considered as retentive of species, is not common to us and other animals. For species are not retained in the sensitive part of the soul only, but rather in the body and soul united, since the memorative power is the act of some organ. But the intellect in itself is retentive of species, without the association of any corporeal organ. Wherefore the Philosopher says (De Anima iii, 4) that "the soul is the seat of the species, not the whole soul, but the intellect."
Memoria, secundum quod est conservativa specierum, non est nobis pecoribusque communis. Species enim conservantur non in parte animae sensitiva tantum, sed magis in coniuncto, cum vis memorativa sit actus organi cuiusdam. Sed intellectus secundum seipsum est conservativus specierum, praeter concomitantiam organi corporalis. Unde philosophus dicit, in III de anima, quod "anima est locus specierum, non tota, sed intellectus".
For what is received into something is received according to the conditions of the recipient. But the intellect is of a more stable nature, and is more immovable than corporeal nature. If, therefore, corporeal matter holds the forms which it receives, not only while it actually does something through them, but also after ceasing to act through them, much more cogent reason is there for the intellect to receive the species unchangeably and lastingly, whether it receive them from things sensible, or derive them from some superior intellect.
Quod enim recipitur in aliquo, recipitur in eo secundum modum recipientis. Intellectus autem est magis stabilis naturae et immobilis, quam materia corporalis. Si ergo materia corporalis formas quas recipit, non solum tenet dum per eas agit in actu, sed etiam postquam agere per eas cessaverit, multo fortius intellectus immobiliter et inamissibiliter recipit species intelligibiles, sive a sensibilibus acceptas, sive etiam ab aliquo superiori intellectu effluxas.
Thus, therefore, if we take memory only for the power of retaining species, we must say that it is in the intellectual part. But if in the notion of memory we include its object to be something past, as past, then the memory is not in the intellectual, but only in the sensitive part, which apprehends individual things. For the past, as past, is something individual, since it signifies being under a particular condition of fixed time.
Sic igitur, si memoria accipiatur solum pro vi conservativa specierum, oportet dicere memoriam esse in intellectiva parte. Si vero de ratione memoriae sit quod eius obiectum sit praeteritum, ut praeteritum, memoria in parte intellectiva non erit, sed sensitiva tantum, quae est apprehensiva particularium. Praeteritum enim, ut praeteritum, cum significet esse sub determinato tempore, ad conditionem particularis pertinet.
The condition of past may be referred to two things: namely, to the object which is known, and to the act of knowledge. These two are found together in the sensitive part, which apprehends something from the fact of its being immuted by a present sensible, wherefore at the same time an animal remembers to have sensed before in the past, and to have sensed some past sensible thing.
Praeteritio potest ad duo referri, scilicet ad obiectum quod cognoscitur; et ad cognitionis actum. Quae quidem duo simul coniunguntur in parte sensitiva, quae est apprehensiva alicuius per hoc quod immutatur a praesenti sensibili, unde simul animal memoratur se prius sensisse in praeterito, et se sensisse quoddam praeteritum sensibile.
But as concerns the intellectual part, the past is accidental, and is not in itself a part of the object of the intellect. For the intellect understands man, as man; and to man, as man, it is accidental that he exist in the present, past, or future. But on the part of the act, the condition of past, even as such, may be understood to be in the intellect, as well as in the senses. Because our soul's act of understanding is an individual act, existing in this or that time, inasmuch as a man is said to understand now, or yesterday, or tomorrow.
Sed quantum ad partem intellectivam pertinet, praeteritio accidit, et non per se convenit, ex parte obiecti intellectus. Intelligit enim intellectus hominem, inquantum est homo; homini autem, inquantum est homo, accidit vel in praesenti vel in praeterito vel in futuro esse. Ex parte vero actus, praeteritio per se accipi potest etiam in intellectu, sicut in sensu. Quia intelligere animae nostrae est quidam particularis actus, in hoc vel in illo tempore existens, secundum quod dicitur homo intelligere nunc vel heri vel cras.
And this is not incompatible with the intellectual nature: for such an act of understanding, though something individual, is yet an immaterial act, as we have said above of the intellect (Q76, A1); and therefore, as the intellect understands itself, though it be itself an individual intellect, so also it understands its act of understanding, which is an individual act, in the past, present, or future.
Et hoc non repugnat intellectualitati, quia huiusmodi intelligere, quamvis sit quoddam particulare, tamen est immaterialis actus, ut supra de intellectu dictum est; et ideo sicut intelligit seipsum intellectus, quamvis ipse sit quidam singularis intellectus, ita intelligit suum intelligere, quod est singularis actus vel in praeterito vel in praesenti vel in futuro existens.
In this way, then, the notion of memory, in as far as it regards past events, is preserved in the intellect, forasmuch as it understands that it previously understood: but not in the sense that it understands the past as something "here" and "now."
Sic igitur salvatur ratio memoriae, quantum ad hoc quod est praeteritorum, in intellectu, secundum quod intelligit se prius intellexisse, non autem secundum quod intelligit praeteritum, prout est hic et nunc.
Augustine says (De Trin. x, 11) that "memory, understanding, and will are one mind."
Augustinus dicit, X de Trin., quod "memoria, intelligentia et voluntas sunt una mens".