The form takes parent_entity_id fine and the right one appears but when submitting all is good until I check the pertson entry and it is not associated with any entity.
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Just adding; I don't think the issue previously was with the relationship as I could add the related entity to a person in the backend and if I used the form but actually selected as a user rather than passing the entity ID in a url parameter, it was fine.
The form is not appearing because you asked me to delete and re-establish the relationship and after that the form didn't contain or allow me to add any relationship at all.
SO.... I have restored the site to its state before I did that and updated all plugins. Effectively, the site is back to where we were when I first reported the issue but with plugins up to date as at today
The issue has been reported but our development team hasn't produced a fix for it as yet.
As your relationship is one to one this is a bug on our side that needs to be fixed. The problem is that you shouldn't be able to connect posts that are in previous relationships.
I will update you once there is some fix for this.