The Series 70 1911 (Colts) were redesigned, in the Series 80 pistols to have a internal safety. The Series 70s and 80s do not match up as the 70s do not have, or are not cut for the frame and slide safety parts found in the Series 80. Also, the 22 lr conversion you have may well have had to be fitted to your frame and may not fit the Series 80 pistol frame without being worked and the Series 80 safety may have to be removed to get the 22 conversion to work.
Some folk say you can mix and match the parts but others say it is quite difficult. I think you should run this past the gunnut69, the Moderator for the Gunsmithing Forum and see what he has to say.
Ya know, you can also buy one of the new 1911 style 22s, Browning makes one and so does someone else (Chiappa, I think) and avoid the headaches.