Aim, move site to a different account, for example primary or seconday(addon) domain to a new DirectAdmin account.

Here is what i did and what worked:
- Backup original domain (backup section, select domain to backup, let ticked all options. Download backup.
- Delete domain
- Upload backup to new account (File manager/ create folder "backups")
- Restore backup
- Check configuration .php files (for example mysql login credentials) and replace old username by new username. Maybe change PHP version if you had non default one.