Hi Andrea 

Providing you have the version of Moodle required to upgrade to the equivalent Totara as detailed in the Upgrading from Moodle docs then the whole database will upgrade including all users, progress and courses.

If you have customisations in Moodle then the custom code will need to be merged. If you are using third party plugins then these should work as detailed in Moodle plugins docs 

If you only have a few courses to move over then a course backup with user data will be able to be restored into Totara.

Course completion and user uploads are possible in Totara if required - HR import can be used in Totara to populate the user, Jobs, organisation and  position hierarchies 

It is a good idea to discuss the migration with a Totara Partner who can discuss the options that best suits your situation.

regards