> What is more tax efficient?
To work out a complete answer to 'what is tax efficient', tax planners go beyond the current tax year and look to see what the total tax take is over many years and when one uses the money for the purpose it was intended. For example, your question becomes simpler to answer if you said your friend was going to use the proceeds to provide retirement income in Portugal in 10 years time.
Maybe you meant, given the fact that he is living in the UK, is there less tax if he shifts where the assets are held? Given that your fellow is taking up a UK domicile now, and is long term UK resident, at the moment I can't see that there would be any difference in tax. I might have misunderstood your question and context though.
> Is it wise to keep them under a US address or change his address to the UK one as he intends to stay in the UK?
Thinking about it, you might mean simply, shall I tell the company secretary of each share to change the registered address of the owner? Sure. But you are not going to be able to manage the portfolio in this form: you will need to get everything into one nominee and one broker. Fidelity could accept the shares into their nominee name, but I would check to make sure that Fidelity can invest in the securities you may want to trade in - you may find that they exclude Eurobonds, for instance, and Hong Kong and Mumbai registered securities. Many of the private banks and brokers that will deal with new USC clients outside the USA have moved already - to the Far East. If you go to brokers in the UK, such as Charles Stanley and Redmayne and WH Ireland, they will foam at the mouth when you mention 'USCitizen'. If you stay with Fidelity then you have to accept their tax certificates done in the US way, and the need to translate them for your UK tax return, so some would say this is not really convenient. Stockbrokers in Bermuda will provide tax reports both in calendar year and UK financial - that might work better for your friend. Then you have the dealing costs, process (can you take my dealing orders by email?) custody (which bank has custody, how are their records checked) and security of the nominee to consider. Other people have mentioned on this forum Interactive Investors and Raymond James US. Of the two I prefer the latter, but not by much. I think I saw that Edward Jones plans to open in the UK.
At some point you'll want to look at the tax favoured accounts you can wrap your investments in. Some brokers do a mix and match thing (use any account that we've got an understanding with), some insist that you use their IRA, their 401k, their SIP etc. If you want a quick answer for this year. nothing much wrong with Fidelity.