Here's a simple step-by-step guide to move your FusionInvoice installation to a new host:
Export your whole FusionInvoice database from the current provider. You can do this straight from FusionInvoice in the settings menu, or use a database admin tool like PHPMyAdmin or MySQL WorkBench.
Compress all of your FusionInvoice directory files from the old provider into a zip file.
At the new provider, create new database.
Import the data that you exported from the old database into the new one.
Upload the zip file of your files to the new provider and extract its contents.
Edit the /config/database.php file to target your newly set up database.
Clear your caches by removing all files from these directories:
Log back in. Your FusionInvoice should now be up and running at the new location.