This is a complex question. Jimmy wanted to go straight and to marry Annabel Adams. He no longer needs his custom-made safecracking tools, but he probably should have dumped them in some river rather than planning to give them away. If he was really going straight, he shouldn't have encouraged some other person to use them for criminal activities. Furthermore, many investigators like Ben Price would assume that Jimmy had been guilty of burglaries he never committed. The tools left unique marks and damage. When Ben Price investigated the three bank jobs Jimmy had pulled off since his release from prison, he studied the safes and said to himself:

“That's Dandy Jim Valentine's autograph. He's resumed business. Look at that combination knob—jerked out as easy as pulling up a radish in wet weather. He's got the only clamps that can do it. And look how clean those tumblers were punched out! Jimmy never has to drill but one hole. Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness.”

In other words, the tools can be used as evidence to convict him of the three jobs he has already committed, and they could be used as evidence against him for any future jobs that might be pulled off with those tools. So it doesn't make good sense for him to be giving them to some old pal named Billy.

On the other hand, O. Henry wanted to have a scene in which Jimmy opens a supposedly burglar-proof bank vault in order to release a little girl trapped inside. So Jimmy had to still have possession of those specialized tools. He writes a letter to his friend Billy in which he says:

I want you to be at Sullivan's place, in Little Rock, next Wednesday night, at nine o'clock. I want you to wind up some little matters for me. And, also, I want to make you a present of my kit of tools. I know you'll be glad to get them—you couldn't duplicate the lot for a thousand dollars.

Jimmy is going to take his suitcase full of tools to Little Rock, Arkansas, on the morning the little girl accidentally gets locked in the bank vault. That is why Jimmy finds himself in that room with Annabel and her entire family present. He feels compelled to expose himself as a professional safecracker by opening his suitcase and using his tools to open the vault. O. Henry probably couldn't think of any other way to handle that scene. Jimmy had to be there when the little girl got locked in the vault, and he had to have his special tools with him, because even Jimmy Valentine couldn't open that brand-new, state-of-the-art vault without those tools. He is being driven to the train depot in his own horse-and buggy by Dolph Gibson, who is waiting for him outside the bank as agreed. He probably takes the suitcase with him when he is invited to come inside with the others to look at the new bank-vault because he doesn't want to risk having anybody, including Dolph Gibson, opening it and seeing what is inside. 

So Jimmy is able to save the little girl, but he has to expose himself as an expert safecracker with highly specialized tools. And Ben Price is waiting for him right inside the bank. Price planned to arrest Jimmy but never expected to catch him red-handed cracking a bank vault with his complete set of incriminating tools.

Jimmy wanted to get rid of his tools, but he shouldn't have thought of giving them to his old pal. On the other hand, if he wasn't taking them to Little Rock that day to hand over to Billy, he wouldn't have had them to open Annabel's father's bank vault, and the little girl would have died. Ben Price lets Jimmy go free after seeing his heroic sacrifice. O. Henry does not tell how Jimmy is going to explain things to his fiancee, her father and mother, and her other relatives. Probably Jimmy will have to confess that he is not really Ralph Spencer and that he used to be a crook but has reformed. Hopefully Annabel loves him enough to forgive and forget, and her family goes along with her in letting the marriage proceed and letting Jimmy remain Ralph Spencer the successful Elmore businessman.

O. Henry does not explain what happened to the tools and the suitcase. We can presume that both were destroyed.