If you are asking if those sentences are correct, yes they are, and they often have the same meaning. I know that can be confusing with the exchange between "am" and "was."
Though they can mean the same thing, here is a time when they do not:
"I told him that I am going to send the money very soon," always means that the action of sending the money is still in the future.
"I told him that I was going to send the money very soon," can mean you are going to send it in the future, you have already now sent it, or that you can no longer send it because something has changed.
Examples:
"I told him that I was going to send the money very soon, and I will send it as soon as I get my paycheck."
"I told him that I was going to send the money very soon, and then I sent it later that day."
"I told him that I was going to send the money very soon, but then I was robbed and now I can not."
If you were saying this last one out loud, you would show the difference by an emphasis on the first was.