Cornelius’s prayers (no difference is intended between προσευχαί in this verse and δεόμενος in v. 2) and his charitable gifts ἀνέβησαν εἰς μνημόσυνον (cf. v. 31, ἐμνήσθησαν, with no difference in meaning). Cf. Mt.
26:13; Mk 14:9, λαληθήσεται εἰς μνημόσυνον, and, for ἀνέβησαν also, Targum Esther 6:1 (In that night
there went up (or perhaps in, על) the memory (דכרן)
of Abraham, Isaac, and Jacob before their Father who is in heaven, that there
should be sent from on high an angel, Michael, chief of the army of Israel).
The actions referred to will be brought into memory, be remembered; here (and
possibly in Mt. and Mk also), before, that is, by, God. In the OT such
remembering is often the effect of a sacrifice (e.g. Lev. 6:8 (LXX), ὀσμὴ εὐωδίας, τὸ μνημόσυνον αὐτῆς τῷ κυρίῳ), but the thought is widened; cf. Ps.
141:2; Sirach 35:16f.; Tobit 12:12; Phil. 4:18; Heb. 13:15f. For the double
sense of remembering (men remember with gratitude God’s gracious acts; God
remembers men in their need) see Le Déaut (Nuit
Pascale 70f.). Here the latter sense is intended; God is about to take
action on behalf of Cornelius by bringing him within reach of the Gospel. He
does this, one might say, because Cornelius has shown by his devotion and his
charity that he deserves it. This theme runs through the narrative; it is
reasonable to ask whether it is consistent with, for example, Pauline theology.
(C. K. Barrett, A Critical and Exegetical Commentary on the Acts of
the Apostles [International Critical Commentary; Edinburgh: T&T Clark,
2004], 502-3)