HI, thanks for the quick response. I did not have time up until now to try.
MMmh, I thought there is the option to download the file and execute it in the app, and then there is an prompt which said something like: “…failed…”. But anyway, as long as it works in the end…
I did that:
user@linux$ fastboot --set-active=a
Setting current slot to ‘a’…
OKAY [ 0.022s]
finished. total time: 0.022s
user@linux$ fastboot getvar current-slot
current-slot: a
finished. total time: 0.020s
BUT
user@linux$ fastboot boot twrp-3.4.0-0-FP3.img
downloading ‘boot.img’…
OKAY [ 0.787s]
booting…
FAILED (remote: unknown reason)
finished. total time: 2.265s
I tried and strangely, it worked
user@linux$ fastboot --set-active=b
Setting current slot to ‘b’…
OKAY [ 0.022s]
finished. total time: 0.022s
user@linux$ fastboot boot twrp-3.4.0-0-FP3.img
downloading ‘boot.img’…
OKAY [ 0.774s]
booting…
OKAY [ 8.600s]
finished. total time: 9.374s
Following your instructions from (TWRP installable stock firmware packages for Fairphone 3 ) I reinstalled the stock rom, did factory reset, ran magisk.zip to root and last flashed twrp, left the oem unlocked for now and ignore the warning during the boot.
(fyi: in the first run i didn’t flash twrp, just booted it and locked oem, with the stock recovery lastly, but came to the same dead-end as in the beginning of the thread)
thought so too, but when you are desperate… 
Yeah I read, when unzipped you can flash every part.
fastboot flash boot boot.img
fastboot flash system system.img
etc.