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I found out from looking at the catches from my hosted den frame that the potential to have an Egg Move is preserved. If one has it, they all will, but only if the Star of the mon is 4 or 5. If it's 3, it's a different moveset. That's interesting because I figured Raidfinder would've covered it by now whether a frame comes with an Egg Move or not.
That being said, here are the Egg Moves for my den, if anyone wants me to pull one of them up to host.
Linoone (4* Sample, Knock Off)
Greedent (5* Sample, Belly Drum)
Dubwool (5* Sample, Counter)
Diggersby (4* Sample, Rollout)
Oranguru (5* Sample, Dream Eater)
Snorlax (5* Sample, Fissure)