Would backing up your server and bring up a new copy from that backup work for you?
As @Yosu_Cadilla suggests, back up your database and files, move server, set up your new database and import. Do you need some guidance to do this?
You may need to tweak the settings in your config files to reflect the new server setup (for example if you have a different database user/password, or table prefix).
On that same line of thought, here’s a post I made some time ago about backing up Mautic.
Sadly I never wrote the “recover from the backup” article, if this is something that would be helpful to you don’t hesitate to ask and I’ll accelerate that content: