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Welcome to the forum, you might want to have a look at the following FAQ which explains where everything is
Welcome to Benefits and Work In case you are not aware, your real name appears to be showing in the forum, if you want to change this then follow the instructions in the following FAQ
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Your ESA will end when you reach State Retirement Age and your CA (but not your wife's) will cease payment although you retain an underlying entitlement.
Your wife may be able to claim New Style ESA providing her GP is willing to provide a Fit Note and she has been claiming CA during the Tax Years 2017-18 and 2018-19, failing that she may be able to claim Universal Credit, either as a carer or as unfit for work.
You can get a better idea of what you might be entitled to by putting your information into one of the online benefit calculators.
www.gov.uk/benefits-calculators Gordon