It says here
https://www.gov.uk/uk-family-visa/knowledge-of-english
If you want to settle permanently in the UK within 5 years
If you took the CEFR A1 when you first applied for your visa, you’ll need to take a CEFR A2 test when you apply to stay after 2.5 years.
If you did not need to do the CEFR A1 when you first applied for your visa but you need to do it now, you’ll need to pass it when you apply to stay after 2.5 years.
I do not know if your wife was exempted but it might be safer to do the English test. It is quite a hassle when your visa is rejected because of a simple English test.
Maybe someone more knowledgeable can provide a more accurate answer to your question.