MacBook Air Early 2015 SSD > MacBook Pro Early 2013? BLUF: Can I use the SSD out of a MacBook Air in a MacBook Pro 13?

I have a road worn but otherwise fine MacBook Pro 13"/Early 2013. About a year ago it started having issues with crashes and hangs. I reformatted its drive and reinstalled macOS, which worked for a little while. But now that machine will not fully POST. It will boot, but almost immediately indicates that it can't find a startup disk. That indicates an SSD failure to me.

I happen to have an Air, but I'd rather have the Pro up and running——so can I swap out the drives? Both were running identical versions of Mojave.
Have you tried reverting to the original macOS that was shipped with this system? If you can reproduce the same behavior with Mavericks/Yosemite then you could very well confirm that this behavior is rooted in an SSD failure vs file system issue. 

This blog post lists a number of issues as to why Mojave cannot find your hard disk, I would perform a systematic check before trying to swap out the hard disk.