I do not know for all airlines but for
- BA : nothing needed, just say your companion has an exemption
- LH : need a COVID test in a good timing (24h prior to departure I think) + a doctor's note

I forgot to say that the doctor's note must be on a specific form: https://www.lufthansa.com/content/da...0220622-EN.pdf
And that the test must be a PCR (and it is 48 hours prior depature, not 24 hours)
https://www.lufthansa.com/xx/en/exem...uth-nose-cover