Fixed penalty notice

[Aratron]

I drove a replacement car about 3 weeks ago on returning the vehicle i threw an apple core out of the window and about two weeks later the garage called me to say that they had been given a fpn for the offence I informed the council that I was responsible and I am waiting for the fpn to be served to me.
Is there a time limit to all of this or can they just service it whenever they want to ??!