What is the ruling on continuing studies in another branch of the institute after paying the remaining collected fees?

The contract between the student and the institute is a lease contract for a permissible educational service according to Sharia. The agreed-upon fee is binding on the student even if they do not study, as long as the institute has provided the agreed-upon service. A lease contract is not rescinded by one party's termination unless there is an excuse that affects the subject of the contract, which is the teaching, and no excuse has arisen to prevent it. Transferring from one branch to another is permissible by agreement of both parties.