The wreck of the SS Richard Montgomery was surveyed by divers in 2003, and by high-resolution multi-beam sonar survey in 2005 and September 2006. The 2003 diver survey comprised an ultra-sonic hull-thickness survey, as well as a visual inspection. The report of this survey is available on the Maritime and Coastguard Agency website.
From these surveys it does not appear that the wreck of the SS Richard Montgomery has moved.