Is there anyway I can move the whole XOOPS installation including all the information written to the database to another server?

yes....
you'll need to back up the database (export it)...

import the database at the new host...

Copy ALL files and directories from the current host to the new host....

Open and edit mainfile.php to reflect the new source root and database info...

all done!

I recommend using the same database name as your current host, as this will cause some issues if the names vary.
Also, some modules use the root path of your server for information...re-install or update any modules you find geeking out after the move.

info on saving your database etc is available here;
https://xoops.org/modules/smartfaq/category.php?categoryid=23

Good luck! & Happy Xoopsing!