Is it permissible to take a fine from a thief – in addition to the stolen money – in exchange for his betrayal of trust and friendship, and is this lawful or unlawful?

If the fine is for breach of trust and neighbor's rights, then it is not permissible to take it, and the ruling for it is void. You are only entitled to what he stole from you.

However, if he returned some of what he stole and denied some of it, and a reconciliation was reached between you based on that denial, then it is permissible for you to take the thousand (currency unit) as a settlement for that, for "reconciliation is better," and arbitration is permissible in financial matters and the like. Reconciliation is permissible even with denial.