Upvote:1
That's almost the same situation than Transit visa requirements while traveling from US to India with stops in Heathrow and Frankfurt except your wife is a permanent resident in the US.
Just as in the other case, she would be exempted from any airport transit visa requirement in the Schengen area based on her permanent resident status in the US. As London is not in the Schengen area, the flight will depart from the international part of the airport and visa-free transfer should be possible. See also Transit visa travelling from Canada to India via Germany or Do I need a visa to transit (or layover) in the Schengen area?
In the UK, she would also be exempted from the direct airside transit visa requirement based on her status in the US, if she holds a “US permanent residence card issued on or after 21 April 1998”. See gov.uk