Yes, it needs to arrive or be deemed to arive by 4/7, so if dated 7/7 it clearly can’t.
Presumably the first PCN issued and the V5C is correct so it wasn’t sent somewhere else first. Usually they don’t bother checking anyway.
They print the usual rubbish about “we may recover from you, the keeper, on the assumption that you were the driver” and whilst they can assume what they like, this assumption has no legal force because of the PoFA 2012 failure.
An appeal will probably lead to a rejection, followed by a rejection at the IAS, followed by a county court claim. I’m not sure how much history exists on the forum for London Parking Solutions, but many cases get discontinued if defended prior to the claimant having to pay the court fee. In particular, they seem to engage DCB Legal who almost always discontinue, but warn your friend that whilst the begging letters from DCBL can be ignored, DCB Legal and its Letter of Claim should be responded to. And that the driver should never be identified, and that no telephone calls should be made or accepted.
Plus no “period of parking” as you also note. So a simple defence based on this and the issue date will suffice in due course.