Pay the Registration twice?

Anyone ever experience having to register their leased car in a new state and being forced to pay the new state’s registration fee to the leasing company? I leased a honda accord in florida last year, just moved up to NJ and was told at the dmv to contact Honda…Honda just got back to me saying it will cost me $600 to register the car in NJ. Does this seem wrong?

Leasee should be responsible for registerstion. Seems odd that Honda would need to pay it and then bill you, but I guess they are the legal owner.