If Joe steals Alice's widget, but Alice for some reason doesn't want Joe to be convicted and is okay with him having her widget, can she retroactively give him permission? Does this prevent him from being prosecuted?
Yes, but that doesn't make the theft not theft
At the time of the crime, Joe committed theft. The state can prosecute Joe for that theft. Alice's subsequent gift does not change this although it would prevent her from suing for recovery.
As a practical matter, if Alice was willing to lie and say that the gift preceded the theft or she had given permission for the item to be taken, this would almost surely create reasonable doubt in any prosecution. However, on a pure "these are the facts" basis, the theft is a theft.
It is a statutory defence to a charge of theft for Joe to show that 'he appropriates the property in the belief that he would have the other's [Alice's] consent if the other knew of the appropriation and the circumstances of it.' (Theft Act 1968, section 2(1)(b)). The fact that Alice did give consent once she knew of the appropriation and its circumstances would be pretty helpful to Joe here.
I'll rephrase the question for clarity.
Assume the defence and prosecution submit the following joint agreed statement of facts:
- at 20:00 Y owned the Item
- at 20:00, X took the Item from Y
- when X took the Item from Y, X did not have permission to take the Item from Y
- when X took the Item from Y, X did not believe X had a right to possess the Item
- when X took the Item from Y, X intended to deprive Y of the Item
- at time 22:00, Y gave X permission to possess the Item
Is theft made out on these facts?
Yes. Whether an offence has been committed is assessed based on the circumstances at the time of the alleged offence. All the elements of theft are present for the act that occurred at 20:00.
It is not open in law to argue that consent provided at 22:00 could have any bearing on the guilt, if it is established that when the item was taken it was taken without consent.
This is so basic a proposition that I can find only one example where the defence attempted to argue that the complainant could provide retroactive consent to erase an element of an offence otherwise established. The court decided based on credibility, but was also highly skeptical that such an argument would even be legally available. See R. v. Baksh, 2008 ONCA 116.