I think as long as you start the research while it's available, you can take your time finishing it?
WickedLazy That has been the case with Mew and Celebi however Niantic have said this special research is limited time only, presumably only lasting until the end of the event. So you won’t be able to take your time with it.
I am also going to post this again because it is very important:
For anyone getting others to log in for them in another location, be very careful. Niantic is cracking down hard on cheating and spoofing.
Just make sure you leave enough travel time. So if your friend logs out of your account at 3.00pm in another town, don’t log in in your hometown until the time it would take you to get back there, else it will flag up.
So if it takes 40 minutes to get back, wait at least 40 minutes (if not more).
Many accounts have been banned because trainers got others to log in for them in a different location.