Migrate the posts of a category to another blog as a custom taxonomy

I'm running a multisite WordPress, and I need to so the following migration between 2 blogs:

1. All the posts of a sub-category X that has the parent category programs from the blog A.
2. To the blog B under a sub-taxonomy X that has a parent custom taxonomy programs.
3. Blog A doesn't have the taxonomy programs, it only has it as a parent category.
4. Blog B has the taxonomy programs already created, but doesn't have it as a category.
5. And I need to migrate all the posts' related data and fields.

I tried to use some export/import plugins, but none helped. I always was stuck at the point of the taxonomy types switch, and the similarity between the slug of the origin category in blog A and the target taxonomy in blog B.

Any idea how to do it, please? And what are the steps or plugins that I have to use?