Hi, thank you for your question. He will need to make an application to find out if there has been a decree absolute (final order of divorce) in England (here: https://www.gov.uk/copy-decree-absolute-final-order) or the US as if there has been no divorce or nullity then he is still legally married and he cannot remarry.
In the event that he cannot obtain such confirmation he can pursue an application for nullity due to non-consummation of the marriage - the guidance can be found here: https://www.gov.uk/how-to-annul-marriage/when-you-can-annul-a-marriage
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A colleague has also pointed out that it will be easier for him to pursue a divorce under five year separation instead of nullity in the event that he cannot ascertain whether there has been a divorce. The divorce process can be found here: https://www.gov.uk/divorce/overview
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Yes, if it is true that she had not divorced her first husband and then married your partner, then the marriage is void and he can seek to annul the marriage and he will require the annulment to marry you.