Warning: I was wrong about phone pics of the moon being fake

I used to roll my eyes at every moon shot posted from a phone. Figured there was no way a tiny lens could pull that off, so I assumed people were faking it or just reposting stuff from a real telescope. Then last week a guy at our astronomy club meeting in Tucson pulled out his phone and showed me his raw files from a night out at Gates Pass. He walked me through it: the moon is stupid bright, so with the right exposure settings, about 1/125 sec at ISO 100 on a manual mode app, you can catch craters with a plain phone on a tripod. What really got me was his before and after, the unedited frame looked like a white blob with faint gray patches, and after stacking 40 shots in free software the sharp version popped out. I sat there kind of embarrassed because I had been quietly judging those posts for years. Now I want to try it myself before the next clear night, but I have no idea where to start with the stacking part. Has anyone here stacked phone moon shots and got a decent result, and what app did you use?