No internet while using android phone mobile data

The thing looks strange:
My laptop detects and connects to the android phone hotspot.
Yet, it works well only when the phone itself is connected to any WIFI (like the one I use at home)
If I wish to use android phone mobile data (instead of regular wifi), my computer is still connected to the phone hotspot, but it does not connect with the internet.
Thing is, I have no similar problem working on another laptop under debian…

Any suggestions more than welcome!
L.