Yes, sure, you can transfer the production from one machine to another and is quite simple.
You will have to dump the downloader_history, l1_tile_history, product and lpis tables (I hope I did not missed anything) from the old server and then import them into the new one’s database with something like this:
pg_dump -U postgres -Fc sen4cap -t <table_name> > /path_to_dump/<table_name>
pg_restore --clean -U postgres -d sen4cap -t <table_name> /path_to_dump/<table_name>.sql
Before doing the import you should also copy the products from the old server to the new one, in the same locations :
All directories /mnt/archive/<site_short_name>
And optionally (but if the new system is already installed, you had to provide them during the installation) gipp_maja, srtm and swbd directories.
Of course, you will have to make sure that all the above directories have write access for the user sen2agri-service otherwise the new installation will not be able to write into them.
Please note that you should use the same system version on the two servers when you will do the switch otherwise you can get to unpredictable results (so if you use 2.0 on the new one and the old one is 1.3, you should upgrade first the 1.3 to 2.0).
Hope this helps.