Elon Musk is now facing a lawsuit in connection with the takeover of Twitter.

A Twitter shareholder accuses Musk of "unlawful conduct" and is demanding damages.

He cites several points: Musk had engaged in "market manipulation" by only belatedly making his entry on Twitter public at the beginning of April.

He also raised doubts about the takeover with his most recent statements and thus drove Twitter's share price down.

He wanted to put himself in a position to drop the transaction or renegotiate the price again.

Musk and Twitter originally agreed on a price of $44 billion.

But about two weeks ago, Musk said the transaction was "on hold," while asking Twitter for more information about the number of accounts with no real users.

The share price of Twitter has since lost significantly in value.

The lawsuit was filed on behalf of all Twitter shareholders, so as a possible class action.

Not only Musk is named as a defendant, but also Twitter itself.