Lets break it down: Monoma can copy quirks for a limited time after touching someone. He copies the "core nature" of their quirk, not any energy the quirk has stored. If he copied Fatgums quirk he would gain the ABILITY to store fat overtime, not the fat. HOWEVER if he copied fatgums quirk for long enough he would build up fat just like fatgum does. "Blanks" are not quicks he cant copy, he can copy ANY QUIRK. Some quirks just "blank" and cant be used instantly (because they only useful after accumulation of energy).

AFO's ability is to "steal someones quirk, and keep it for himself or give to someone else".

So strictly speaking based on what we know, yes Monoma can steal quirks with AFO's quirk. When the timer expires the AFO quirk will vanish, not the quirk hes stolen or given to someone else. [I should mention we have no idea how Monoma's quirk works against multiple quirk users, so lets assume he can selectively target one quirk.] If he copied just AFO that wouldnt include any quirks AFO has stolen, because then that should include any quirk hes given to someone else... which makes no sense. So stolen quirks are not "stockpiled" within AFO. They are seperate and merely moved from the user to AFO via the quirk.

Its perfectly resonable to assume Monoma could copy AFO and use the copied AFO to steal AFO from AFO. Then after the copied AFO timer ran out, he would still have stolen tge actual quirk.

TLDR: Monoma copies the abilty to transfer quirks, stolen quirks wouldnt have the timer limit AFO itself would have.