xonus Of course I can install the system without the ssd internal, but I wonder why it happens this way and not otherwise
I don't know. It just does. I assume that it has something to do with the way Solus's Linux Boot Manager handles two installations of an identical OS, but that is just guessing.
By the way, riffer's method is a lot simpler, assuming that your internal Solus drive is an SSD rather than an M.2. I've done that, too, and it works just fine. It doesn't make any difference whether the external (portable) drive is internal or external when you install, so long as it is the only available target drive.
The key is to have the external (portable) drive the only drive available as a target when installing. As I understand it, that is the norm for installing Linux on an external hard drive, although it might not be absolutely necessary.
If you want a really simple method of building a test environment, install Solus as a Gnome Boxes or Virtual Box VM on your primary Solus build. Do that, and you can have a test environment for each of the Solus DE's, no fuss, no muss.