If I read right there isnt a task per se in the email, theres just information in there you want to keep, the transferring of the information itself is the task. Personally I would just consider this as processing and do it several times a day. To mark a task to do this is just creating work for the sake of keeping things tidy.

Ppl get hung up on zero inboxes - the point isnt that it stays at zero, the point is that each time you process it you get to zero. My inbox, physical and virtual, are rarely empty, I have so much work coming my way. But i process it at least twice a day, each time i hit the bottom.

If i were you I would just leave them there while I got on with my work, then when I was processing the emails I would transfer the information as part of clearing the inbox, then probably archive them afterwards.