The Spiegel Online article on the subject implied that the two other German parties within the ECR group (ALFA and the Family Party of Germany) have pushed hard for this.
I can imagine that the relationship between the ALFA MPs and the remaining AfD MPs must have been somewhat... strained.
Anyway, it will be interesting to see whether they will choose to go to ENF or EFD now. I think EFD, as the less radical choice, is more likely, but at the same time AfD and the FPÖ have been relatively close recently, and AfD, as a fairly pro-Russian party, might feel more at home in ENF (which is full of pro-Russian parties, except for the Dutch PVV) than in the relatively pro-Atlantic EFD group.
I guess joining ENF would be the end of AfD even trying to appear as ''moderate''.