Yes, other directors can sue a director on behalf of the company. Shareholders can also take legal action to recover losses against an individual director or an entire board of directors for breach of duty, but it must be brought in the company’s name and to recover the company’s loss.
The shareholder is not claiming in their own name for their own loss, but in the company’s name for the company’s loss. Therefore, any sum recovered goes to the company, and it is the board’s decision whether to pass the benefit on to shareholders in dividends.