Reverse charge on rent

A shopkeeper registered under GST pays rent for the shop to the landlord of the shop who is unregistered under gst and the rent is 20,000/- per month. now since the landlord doesn't give a rent receipt with GST will the shopkeeper be required to pay GST in the form of reverse charge to the govt. Also if the shop keeper is registered under composition rule will he get the input credit for reverse charge if applicable. will it be better for the shopkeeper to migrate to normal GST instead of composition if no input credit on reverse charge can be availed?