Done!
The directory in ST16S (520!), where the exports are stored is: /data/media/0/DataPilot/Missions
The format of files is the same as in the QGroundControl for Windows.
Select a provider, download wanted tiles, export the database. By default there: Documents\QGroundControl\Missions
Copy the wanted DB's to the mentioned directory in the ST16S.
Change permissions and, if you want the group and the owner too. For example. The first is exported from the ST, the second is injected by me.
-rw-rw-r-- media_rw media_rw 2367488 2021-12-19 17:37 123.qgctiledb
-rw-rw-r-- root root 49967104 2021-12-19 19:46 def.qgctiledb
All this is accessible via adb shell su.
The process can be automated via script. If someone wants this, let do it.