@Torenaga I'm not sure what template you're referring to, the fact of that matter is TFL will send a notice of rejection no matter what you say. You've also left this quite late, so you'll have to send the letter by special delivery (if you send it first class and it doesn't get there in time for the deadline, your brother could end up owing £240 and have no right of appeal).
Here's a basic draft:
Dear Transport for London,
I challenge liability on the basis that the alleged contravention did not occur.
Furthermore, I contend that the inordinate delay in serving the notice of rejection shows that the authority has failed to have regard to the statutory guidance which provides that "The NtO may be issued 28 days after serving the penalty charge, and we expect authorities to send them within 56 days. The ultimate time limit, in exceptional circumstances, is 6 months from the ‘relevant date’. There should be a very good reason for waiting that long to serve an NtO".
In failing to take this guidance into account, the authority has failed to comply with the requirement imposed by section 87(2) of the Traffic Management Act 2004, and that is a procedural impropriety.
It follows that the penalty charge notice must be cancelled.
Yours faithfully,
Don't forget that the formal representations must come from the registered keeper which I believe is your brother, not you, so he has to sign the representations.