I had a good look at the first link posted above in the end and to the suggested further reading in it, and subsequent links, and it looks as though it is a US concept, conceived in the late nineties/early 2000. That might be why it doesn't feature in current UK training?
It looks as though it is about helping adoptive parents feel like real parents and encouraging them to parent, confidently and competently. It has examples of competent parenting in the first link, and things to think about if you start not feeling "permission" to parent, which are quite wideranging. The link to attachment is that if you do not parent confidently and competently, then that is likely to affect attachment. All of this, set out in the first two pages makes sense, but I do think the chosen words to signify the concept - entitlement and claiming - are slightly unfortunate as it makes it sound as though the child is a piece of lost luggage. And the word "entitlement" often has negative connotations.
However, the final page recommendations in the same link sound slightly misconstrued. Here it is recommended that the adopter creates connection with her child by saying "you look like uncle bob, my brother" or "you draw like aunty joan" - I think that for good MH children need to understand and learn to cope with reality and truth, and I think that this sounds too contrived and invented and as though it could be confusing and unhelpful for a child. As far as I can see there haven't been any studies about its positive (or negative) affect?
I think that like many adoption concepts, this concept is at risk of being lost in translation or misapplied.
Another example is changing the child's name to "claim" - in the US there are arranged adoptions where the birth parent chooses the adopter, and in some cases it is arranged that the adopter will choose the child's name, and this sort of scenario would never happen in a UK adoption as birth parents do not choose the adopter. A concern is that sometimes the child's needs will be different from the adopter's needs. The forums I found about "claiming" were mostly about adoptive parents not "feeling" like a parent and what they could do to help themselves "feel" better.
I think saying "a child needs to be claimed" might be an extrapolation too far, based on what I read.
The book recommended by @sunshineandskyscrapers was one of those recommended in the link and it sounds interesting to read though it is quite old (1995) and therefore in part might be out of date?