Transfer of shares — board approval and registration

A shareholder in a private company limited by shares agrees to sell her 500 fully paid ordinary shares to a buyer. The company has adopted the unamended model articles. The shareholder signs and the buyer takes a stock transfer form. The buyer asks the company to register him as the holder of the shares. The company secretary is unsure of the steps required before the buyer can be entered in the register of members and is concerned that the directors may have a say. Which of the following best describes the position on completing the transfer and registering the buyer?