How to map LSP between XTRF and CAT tool

Hello, I wanted to ask if anyone know how to map an LSP (created specifically in XTM) between XTRF and XTM (but if you managed to do so between different CAT tool, like MemoQ - any advice would be helpful!).

Whenever I try to map the agency profile in XTRF with the LSP in XTM and I run a project with connector in XTRF, a duplicated vendor in XTM is created, instead of assign the existing LSP.

Any advice on how to approach it would be great!

Thanks