At the induction stage I am sure no one will need your admission letter again but however they will need the following information:-
1. Your course of study.
2. Your Allocated student ID number for the fee payment reference.
3. School fee value for the year.
4. University Bank information for the fee remittance.
So as long as its a school you wish to go you can go ahead and give them the above listed details for that school and there shouldn't be any problem at all.