Yes. We must say that the properties are in the persons, and yet that they are the persons because the nature of a form requires it to be "in" that of which it is the form (as we say that the essence is in God, and yet is God).
There are properties in God designated by abstract terms, being forms, as it were, of the persons.
Since relation, considered as really existing in God, is the divine essence Itself, and the essence is the same as person (Q39, A1), relation must necessarily be the same as person.
Person and property are really the same, but differ in concept. Consequently, it does not follow that if one is multiplied, the other must also be multiplied. We must, however, consider that in God, by reason of the divine simplicity, a twofold real identity exists as regards what in creatures are distinct. For, since the divine simplicity excludes the composition of matter and form, it follows that in God the abstract is the same as the concrete, as "Godhead" and "God." And as the divine simplicity excludes the composition of subject and accident, it follows that whatever is attributed to God, is His essence Itself; and so, wisdom and power are the same in God, because they are both in the divine essence.
According to this twofold identity, property in God is the same person. For personal properties are the same as the persons because the abstract and the concrete are the same in God; since they are the subsisting persons themselves, as paternity is the Father Himself, and filiation is the Son, and procession is the Holy Ghost.
But the non-personal properties are the same as the persons according to the other reason of identity, whereby whatever is attributed to God is His own essence. Thus, common spiration is the same as the person of the Father, and the person of the Son; not that it is one self-subsisting person; but that as there is one essence in the two persons, so also there is one property in the two persons (Q30, A2).