@OldaNovak You are right: you cannot sync an Ambit2’s new moves with SA. At the moment that is entirely normal.
MovesLink2 (croc-connector program) isn’t intended to sync with Suunto App at all so you won’t see any new moves there from a sync. As @jw-cou wrote, the transfer copied your existing Movescount data to the SA db which you can review but not, as yet, add to via Suunto App. Check out this recent post.
Pre-Covid-19, Suunto stated that non-BT Ambit users will be able to have a “renewed experience” of functionality via the other cable sync program, SuuntoLink, “by summer 2020”. Check “Compatible watches”, May and November updates here.