Elon Musk's offer has been rejected by Twitter's board.

• According to CNBC's Jim Cramer, Twitter's board has "no choice" but to reject Elon Musk's offer to purchase the company at $54.20 per share.
• Cramer cautioned about the potential "personal liability" if the board approves Musk's offer, valuing the company at approximately $43 billion.

According to CNBC's Jim Cramer, Elon Musk's offer to buy the company at $54.20 per share was rejected by the board, leaving them with "no choice."

Cramer stated on "Squawk on the Street" on Thursday that they have no option but to reject it. If they say "we accept," they are not being truthful, according to him.

The Twitter Board of Directors will meticulously examine the proposal to decide the most advantageous course of action for the company and its stockholders, as stated by the company on Thursday in response to the offer.

Musk's offer to take Tesla private at a valuation of approximately $43 billion could result in personal liability for the board members if they accept it.

Cramer stated that this situation is one where directors are not fulfilling their duties, and there is no fiduciary responsibility if they simply say, "We'll take it." He believes that individual directors can be held accountable for a lack of fiduciary responsibility that goes beyond acceptable boundaries.

A Twitter representative stated that the company had no further comment regarding Musk's proposal.