In order to answer this, let us first define the two terms in this question. The efficient market hypothesis is a hypothesis that deals with stock prices. It holds that stock prices are essentially always equal to their fair market value. All information about a stock’s value becomes available and is quickly integrated into the price of the shares. What this means is that no one can really “beat” the stock market by picking stocks more efficiently than anyone else. The only way to get higher yields is to take larger risks. The concept of shareholder wealth maximization has to do with the duties and objectives of firms. In this view, a firm’s duty is to make the greatest possible wealth for its shareholders.
The concept of market efficiency is relevant to shareholder wealth maximization in at least two ways. First, it establishes that it is not possible to create shareholder wealth by gaming the financial markets. If a firm is going to make wealth for its shareholders, it will have to do so by actually engaging in economic activity that will bring in sufficient revenue. The firm cannot make its shareholders rich by artificially increasing the value of its shares. Second, it is unlikely that the firm’s management would be able to make themselves look good (at the expense of the firm’s financial health) by pumping up the price of the firm’s shares. There are those who worry that corporate management has an incentive to artificially increase share prices to maximize their (the management’s) own pay. If the efficient market hypothesis is correct, this is not possible and therefore people do not have to worry that firms’ management teams are seeking their own economic good instead of maximizing shareholder wealth.