Jamieson, Fausset and Brown on 1 Corinthians 16:3

3. approve by your letters--rather translate, "Whomsoever ye shall approve, them will I send with letters": namely, letters to several persons at Jerusalem, which would be their credentials. There could be no need of letters from them before Paul's coming, if the persons recommended were not to be sent off before it. Literally, "by letters"; an abbreviated expression for "I will send, recommending them by letters" [Grotius]. If English Version be retained, the sense will be, "When I come, I will send those whom by your letters, then to be given them, ye shall approve." But the antithesis (opposition or contrast) to Paul himself (1Co 16:4) favors Grotius' view. So "by" means with (Ro 2:27); and the Greek for "by" is translated, with (2Co 2:4).

liberality--literally, gracious or free gift (2Co 8:4).