For that particular mission he can go through the POIs but unless you manually regenerate them with a console command (in coop) or play on a dedicated server with regeneration enabled, the POIs will be in the same state as you left them. So he won't find any enemies or get any loot except for whatever is given for the mission reward.

It brings up my recent idea. What if it is possible to implement quest POIs in this way: When you has acquired the mission, it says which playfield you should go. When you enter this playfield, the quest-related POI is spawned in certain (maybe a bit random) location. When you are done with the quest and left the playfield, this POI gets deleted.
Of cource, maybe you already thought about this and this didn't work.

Not possible.

I think the idea in coop is to do the missions together at the same time. Or if you already did some then either start a new coop game, or have the friend continue the next mission with you.

Also, it might be best for only one of you to trigger the actual mission steps. Otherwise the missions might glitch, because the coding was designed for single player originally.