He is not obliged to sell his shares , unless company force him to do that.
here is the answer from legal site :
"If an employee or director leaves the company, can they be forced to give up or sell their shares?
In general, shareholders can only be forced to give up or sell shares if the articles of association or some contractual agreement include this requirement.
In practice, private companies often have suitable articles or contracts so that the remaining owner-managers retain control if an individual leaves the company. For example, the articles or contract may say that, if a shareholder wants to dispose of their shares, they must offer them to the other shareholders (usually in proportion to the shares that each already holds) before they can dispose of them to anyone else. In such circumstances, the employee or director may, dependent on the circumstances in which they have left, be entitled to receive a 'fair value' for the shares - often determined by the company's accountants if it cannot be agreed any other way - or may merely be entitled to the nominal value of the shares (eg £1).
The shareholder may have a claim against the company or the other shareholders if they can show that they have been unfairly treated."