I cannot see what is illegal about a syndicate member allowing somebody else to take the controls and log it accordingly.
Obviously the syndicate would not be happy about this usage (against group rules) but that does not mean that it is breaking some law.
One problem would be if the syndicate's insurance is for specified (named) pilots only, in which case this flight would be illegal - because insurance would be void and insurance is mandatory in the EU. But, if the logbook entry is made only after the flight has successfully landed, it's hard to see how this could be detected. Also it is not certain the insurance would be void - the cover might be "authorised pilots" which in this case may well wash.
I used to rent out the TB20 and people used to do all kinds of things with it. One (instructor) claimed to have an ATPL but actually he was a BCPL. One claimed to be an IR Examiner but his IR was lapsed. Etc. Where they actually went I don't know. One of them (an instructor) even claimed the duty drawback and pocketed it - definitely not illegal, possibly not immoral, but stupid because I could have made a duplicate drawback claim and that is illegal.