Lots of conflicting ideas about parrot mouth. But like most genetic defects, it's likely that one gene is received from each parent. So your parrot mouth carrying ram , was mated to your parrot carrying ewes . If each parent contributed ,that gene, you ended up with parrot mouth.
The Math says that they will share that gene with 50 percent of their offspring. Unless they are homozygous for that gene( actual parrot mouth) . Then they transmit that defect gene to all offspring. And if the mother transfers a gene, a parrot will result.
Best practice is to never buy one, never keep one , and never use one.
Others will like weigh in with all the banners won with parrots, and it's a market animal.
Here , as with prolaspe, all offending animals are sold as culls. In my mind, the two problems are usually invloved.
Here at least, lines that produces prolaspe problems, also produces parrot mouth. Culling all invloved rams/ewe solved problem. Keep daughters, and breed them to others that came from parent lines, that had those issues,. Problem came back.
It runs in some lines esp in Suffolk based sheep, but many popular "Hamp" lines ,have been bred from those Suffolk sheep, and the baggage came along.
Good luck.