If he really cannot provide evidence that would qualify him for PR under EEA rules, then I would suggest applying under the 14-year rule (while it still exists).
See
Paragraph 276B.
If the only requirement he cannot satisfy is the English language/KOL. then he may be granted further leave to remain instead of indefinite leave, which would allow him time to complete the course whilst having legal status in the UK. Or he could do the tests before he applies.
An application under the long residence rule should also include evidence of your private and family life to support a grant of discretionary leave as an alternative.
If the application is refused, then you can appeal on the basis of the right to private and family life, and I would also suggest that you can include details of his claims under the EEA rules: if it comes down to it it may be possible to apply for the tribunal to order HMRC to disclose tax details showing when his ex-wife was exercising treaty rights.