Thanks so much for your response!
The owner said that - besides an original replacement of the battery - she never had any repairs done. The phone was visually in fine condition and the watermarkers didn't indicate any kind moisture being present or having been present inside of the devide..
She said the problem of the reboots just started appearing randomly. I'm not sure if she was saying the truth.
When I got the phone it wouldn't even boot into iOS since she was stuck in an upgrade loop + the instability issue (artecafts, random reboots after some minutes). So I fixed it by somehow being lucky with the loop, entering DFU (as you recommended) and installed the latest iOS on it.
After that I could get into the iOS while the problem of random reboots persisted - BUT - the rate in between the reboots diminished from day to day until at one point there where no more reboots and I could use it as a normal *reliable* phone for about 3 months.
Has anyone experienced this before? As if the voltage regulator or something inside the phone had to be conditioned properly ?!
2 weeks ago I got myself a good quality charging cable (anker) and charged it up before heading on a bicycle tour for the day. In the evening I noticed how it again started to bootup randomly again and I couldn't do anything to stop it from doing so. And this has been the status until this day.
I will make sure to try to DFU restore in the coming days (once I have access to a proper wifi) with iOS 11 . Maybe *hopefully* this is just a software issue that had been fixed.
And yes, I could also look into a screen replacement - although I'm certain that the one installed is original and of good quality. But I am aware of the fact, that even original parts can fail.
So, in a couple of days I'll attempt the DFU and if that doesn't cut it I will attempt a screen replacement once I'm back from my bicycle trip (lasting 10 days).
If this then STILL doesn't work I have no other option than to sell the phone as a spare-part holder and to try to forget about the whole thing since replacing the logic board would be financially illogic.
Thanks a lot for your replies and your precious time. I highly appreciate it!