The bank can tell if a check is fake when they see it right? It wouldn't just be deposited then later taken away because it turned out to be fake? (If it's established that the check isn't fake...)
Is it possible for the person who wrote the check to go to their bank & have them cancel the check or reverse it?
Your first paragraph is incorrect - a good forgery cannot be detected before deposit.
Your second paragraph - a stop payment is not good after deposit and the check has cleared.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Checks are negotiable instruments, and as such become order paper to the payee. The payor has certain rights under the Uniform Commercial Code however. One of those rights is he can issue a stop-pay on the check.
This being the digital age however, we now live in the Check 21 era. Check 21 refers to federal legislation that allows for "virtual checks", which no longer requires the physical handling of checks. We've all seen those bank commercials that show people taking pictures of their checks and depositing them; well that's one aspect of Check 21. Another aspect however, which may be good news for you, is it greatly reduces "float" time for the processing of checks, thus greatly eliminating the chance for the payor to issue a stop-pay order on the check. With many banks even, depositing of the check allows for instant transfer of the funds to the depositor's account.
So the legal answer to your question is, while the checkwriter (called the "maker") still have the legal authority to issue a stop-pay, if you quickly run to the bank and deposit the check, it may be a moot point. If the stop-pay order is granted before you deposit the check, the maker is still liable on the underlying obligation of course.