The earliest your wife can apply for an extension is 28 days before her 2nd year anniversary of living here in the UK (just the same when applying for ILR).

Go to this page and check out the form she will use and the guidance notes. https://www.gov.uk/government/public...tner-form-flrm

Is your wife confident enough to pass the English test? Of course applying the ILR is still the best route. If the test and result will be on June, make sure that you have all the documents prepared so you can apply ILR before her visa expires on August.