A band, a famous rock band (The Beatles), decides about pressing probably their last LP. During the recording they don’t get along, but at last they publish it and they break up. The LP is a smash.

Way too long and confusing. Try: "During the recording of their last album, the Beatles break up, only to learn the album is a hit."

I think it is good but you should make it about that they have a smash hit and they all quit but they should regroup because they are really good.
Just a thought.

This re post contains more detail than the original however no further plot elements are introduced and as such this sentence is vague in its meaning.

For clarity I must ask, is this intended to be a logline or a statement of sorts related to a story?

Check out the definition of a log line and its components here:
https://loglines.org/howto/

To help with the construct here are a few key questions that are best answered prior to drafting a logline:

Who is the story about?

What does he or she want?

How will he or she achieve it?

Hope this helps.