Cibo,
Did your friend cut it out and you pick up the frag right the way? If so, it will take long time to open up-they are very sensitive.
YES, they are very hardy, so even if they don't open up, they don't usually die.
I recently cut up many frags, the main colony open up in about 3 days back to it's full glory; the frags open in a week but the medium sized new colony has just recently starting to open up after 10 days. It depends on how rough in the process of divisioning it.
If you do see cyano trying to over take it. Blow them off gently like me touching a girl(may be you would like to go for the rough route-I mean to a girl J/K J/K):afro: - don't. It only irritate the coral more and it will stay close longer.
At least, try to clean it so that the "pimples", where the polyps come out from, will show. Once they are out, you can start to rougher to the body of the coral.
Hope this help you.