Money lender's license transferable?

Business can be transferred, but not the license, as a license is granted to individual or his firm on fulfillment of certain terms and conditions and the constitution of the firm including the financial stability of the owner. Since the constitution and the owners of the business are changed, new license on fulfilling the terms and conditions by the new owner would be required. Of course, NBFC registration would also be required.

Money lender license is not transferable...

It has nothing to do with NBFC. NBFCs are monitored by RBI. No money lending license is required.Money lending license is issued by State Govt, to the individuals and proprietor shops