All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In principle, in an Ijarah (Renting, leasing, hiring), the compensation becomes due upon lessee`s reception of the leased item, and in case any sums were collected before that, then they are regarded as "Earnest payment" i.e. payments deducted from customer before the conclusion of the Murabaha or lease hold property contracts. According to Sharia standards for Islamic Financial Institutions {Standard No.(8)}, "Earnest payment" means, "An amount paid by customer upon request of the bank to ascertain the former`s financial ability and that he can compensate for any harm as a result for his failure to fulfill his obligations." From the perspective of Sharia, "Earnest payment" is a security in favor of the bank in case of possible harm.
Therefore, the bank keeps these sums as a trust until the contract is concluded. In case the contract between the customer and the bank was concluded, the sums are considered part of the price, but if it wasn`t then the bank deducts an amount equal to the actual harm that befell it due to customer`s failure to complete that deal.
In conclusion, it is permissible that the customer offers "Earnest payments" prior to signing the finance lease so long as they are kept at the bank as a trust. And Allah knows best.