Is it permissible to perform the absentee funeral prayer (Salat al-Gha'ib) for a man whose Christian wife claimed he willed to be buried as a Muslim, but then buried him in a Christian cemetery after writing an obituary in which she claimed he had converted to Christianity, knowing that he was a Muslim before that?

The corruption you mentioned supports the idea that, although marriage to a Kitabiyyah (woman of the People of the Book) is permissible, it is better to avoid it, especially if it is in the lands of disbelief. The default assumption is that the man died as a Muslim, and the claim of the Christian woman is not sufficient to prove his apostasy. Therefore, it was obligatory to wash him (ghusl), shroud him (kafan), pray over him (salat al-janazah), and bury him in the Muslim cemeteries. The prayer for the absent (salat al-gha'ib) is not prescribed according to most scholars if the deceased is in the same country. If you can exhume him from his grave, wash him, shroud him, and pray over him, then do so. Otherwise, pray over him at his grave, with you facing the Qiblah. The ghusl and kafan are waived due to the circumstance. If you are unable to do that, there is no harm in adopting the view of those who permit the prayer for the absent person within the same country, because Allah does not burden a soul beyond its capacity.