It depends on the states. Some states issue/renew the DL but place an expiration date on DL that is same as expiration date of yoru immigration
documents (this is the case in PA here). If this is the case for th OP,
then he can not renew his DL. If you explain to the DMV that my greend card
has an experation date but my PR staus does not, they can not understand it
and they do not care.
