Arrowflyer, important to note the advice you give only applies to EASA licenses issued before the 31/21/2020, which is stated clearly in the link and in this case does apply to the poster.
But there will be alot of UK nationals who gained EASA licenses after 01/01/21 who were misdavised by their ATOs who will read this and think the above is applicable.
Another thing to consider is if the poster wants the FI rating on just the UK license or on both EASA and UK licenses.
While the two year validation allows you to fly G reg on an EASA license you can't add a UK Part FCL FI rating to an EASA license, so the UK Part FCL does need to be obtained before the FI course. But a UK Part FCL FI course cannot be used to add a FI rating to an EASA license.
As I understand only ratings that were valid on the EASA license on the 31/12/20 can be transferred to the UK license. So correct me if I am wrong if the FI rating were added to the EASA licesne now it couldn't be transfered to the UK license. However EASA ATO training can/may be recognised for UK PArt FCL ratings until the end of 2022. So if I am not mistaken an EASA FI course and then a test with a dual rated EASA/UK FIE would allow both the FI rating to be added to both the EASA and UK Part FCL licenses. My interpretation of the rules so open to be corrected.