Will residency in EU affect refugee status in the UK

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Hi,

If someone is recognised as a refugee in the UK receives an EEA family permit in an EU state, will that affect their refugee status? Or their HO travel document?

In the 1951 convention travel document, it says, if someone takes up permanent residency in a country which is signatory to the convention, then the travel document must be returned to the Home Office.

Will they consider EEA family permit as permanent residency?

Thank you!