Articles 4 to 8 in Commission Delegated Regulation (EU) 2020/723 of 4 March 2020 apply only to licence validations. Steer clear of those if it is a Part-FCL licence you want. Note the time limit for validations in art 4(3):
"The validation of a licence shall have a validity period, which does
not exceed one year, and its privileges shall only be exercised as
long as the licence remains valid."
If you wish to fly a UK-registered aircraft in non-commercial operations for up to 28 days per calendar year then see art 8(4), to which the above time limit does not apply.
The relevant provisions for a licence conversion, rather than a validation, are in arts 3(b) and 9(2).