This sounds like a great idea in general: if ID questions are getting closed over there that would be upvoted and answered over here, then there's no reason not to deprive those questions' OPs of getting their answers. That said, I'd mention a few caveats we should consider.
I've never spent any time on the Anime & Manga SE, but having seen the type of non-book ID questions that some other SEs get, I'd guess that the quality of ID questions being posted to Anime & Manga was so bad that they eventually had no option but to cut out the canker entirely. We don't want our site to be flooded with crap and lose its reputation as one of the few SE sites to have mostly good quality ID questions without needing draconian rules.
To this end, I'd suggest not setting up a direct migration path which could be used by any five 3k-rep users, but instead relying on the A&M mods to migrate ID questions to us manually. Migration paths have caused issues for other sites in the past: e.g. see Please stop using SoftwareEngineering.SE as your toilet bowl and A friendly reminder: ELL is not EL&U's trash can. Unfortunately, allowing anyone to vote to migrate questions often results in really bad questions being dumped on other sites, essentially passing the buck on the job of closing them.
We should also bear in mind that "good quality" for ID questions is subjective and varies by site. Some sites have very different standards from others on what makes a "good" ID question. So we can't necessarily rely on A&M mods or users to know which of 'their' ID questions we'd want and which we wouldn't. The best way to inform them is by manually flagging migrate-worthy questions on A&M ourselves, with a flag text something like:
Since ID questions are off-topic here, could you migrate this question to Sci-Fi & Fantasy, where it would be considered on-topic and within SFF site standards? (Source: I'm an active user on SFF.)
I can't see any sensible reason for a mod to decline such a flag: if a question would be closed on their site but would be open and well-received on our site, then it's an ideal candidate for migration. This seems to be the best way to ensure that we get only the questions we actually want rather than being flooded with crap. The alternative would be educating the users or mods of A&M on exactly which ID questions we like and which we don't, and then potentially having to complain if they migrate bad ID questions which get downvoted here as well.
The decision on the other end
Of course, the ultimate decision of whether or not to migrate such questions is up to the A&M community and mods. They're the ones who have to do the actual migrating. But again, if they don't want the questions and we do, I can't see any sensible reason for them to refuse. Just remember that if you want a migration path, someone will have to propose that on their meta and get enough support for it there. (If we go by the manual flagging approach I suggested above, then posting on their meta won't be necessary unless for some reason those flags are declined.)