Disclaimer: I cannot be responsible if you loose your data by not following the things I mentioned bellow (especially if you do not use backups).Please note that I did extensive tests where I copied profile between original game and modded one and I did not face single issue.
Also this process requires more skills than just single tapping on display however after some time it will become natural. For the safety measures I strongly recommend to test it between two different devices first (for example tablet and phone, or by using emulators etc.). And always copy first - never move.
This is fairly easy process - you can try it to test it between two different devices if you are not sure and want to test it out first:
1. (optional, works only if you are on original game): link it to twitter, fb or google so your profile will be safe.
2. Copy com.bandainamcoent.dblegends_ww from Android/data/ folder somewhere safe.
3. On secondary device install for example the modded APK.
4. Copy the folder you backup-ed in step 2. into its rightful location.
5. Launch game and grant storage permission.
6. Voila - you have your game.
Some notes: it is always better to have your game backup-ed by linking it to one of those services. That way if you mess up with the wrong copy (for example you erase that backup by accident the game will still be available after using the link option). Also - you can copy your profile from original game to modded one and vice versa HOWEVER if you are using linking option than you don't need to copy your profile from modded version to original because everything you do on modded version is automatically synced to the location which you used for linking option.