There's nothing magical going on here. Rename the file, then use File --> Replace with Layer and assuming the document structure doesn't change, AE should automatically relink all other items. And by all means educate your friend about such basics as file name extensions being a necessity. Even on a Mac Adobe apps have been doing this for years already, so it's highly questionable why he chose not to use this and simply doesn't seem to care.
I personally can't find your "Find -> Replace with Layer" actually, and about my friend he did have the Append File Extension as "always" but once he is giving me the files they're set as just file, not .psd
And he made the entire AE file from scratch but that appears : http://prntscr.com/hktplf
But these layers are linked to one .PSD but I have 2 .PSD, as soon as i'm not adding '.psd' at the end of the file name it's working and everything appears. But can't find a way to replace them.
Here is what I've in the 'file' column http://prntscr.com/hktqdi
Adobe After Effects CC 2018 by the way
Try any software that can batch rename multiple files to add an extension to all together. Try Bridge that come with your cc subscription
Can't make it work it out actually :/