The reader should know Jimmy has changed through direct quotations from the text:
Jimmy Valentine looked into [Abigail's] eyes, forgot what he was, and became another man.
It took the love of an amazing woman to change Jimmy from a criminal into an upstanding citizen. Yes, Jimmy did a "job" that landed him in jail, but he worked hard even in prison (fixing shoes) and never needed to be "watched" in order to assure his good behavior. Further, all of his actions afterward point to the fact the Jimmy is no longer a criminal. Jimmy loves Abigail, and as a result, opens a very successful shoe store in the town and prospered through business and trade in those much-needed goods.
Mr. Ralph Spencer, the phoenix that arose from Jimmy Valentine's ashes--ashes left by the flame of a sudden and alterative attack of love--remained in Elmore, and prospered. He opened a shoe-store and secured a good run of trade.
It is also important to note another particular way that Jimmy uses his past "expertise" in order to become a hero: Jimmy opens an unbreakable safe in order to save a little girl. When the little girl becomes locked inside the safe in an unfortunate accident, everyone is scared and baffled as to how to help. Jimmy shows up as a hero, using his "criminal" skills to save the girl. At the same time, his actions reveal (especially to the detective) who Jimmy really is.
In conclusion, it is also important to realize that the detective, Ben Price, agrees with us about Jimmy's "change" in character. Even though the reader fully expects Price to arrest Jimmy Valentine (turned Ralph Spencer), instead Price reveals that he knows Jimmy's true identity, but values his citizenship and goodness so highly that Price does not make the arrest.