If you export the mo file from the website then it should already have the correct name. In the caase of Finnish this should be sp-fi.mo with the admin side being spa-fi.mo.
But remember that the bulk of the translations come from the SP theme not the core.
As long as the items have been translated then one good way of checking if the core mo file is working is to run the ‘About’ popup as most of those translations come from the core.
Worth noting that using WP_LANG in the config file is no longer supported and should be removed. The correct place in WP to now set your language is on the Settings > General panel.
We should have an update to the core (5.7.5.3) coming over the next few days which will fix the URL issue which came about because the site was moved to a new server.