A sends their open padlock and a box to B. B puts their open padlock in the box, and locks it with A's padlock and sends it back. A opens his padlock, puts the ring inside, locks it with B's padlock and sends it back.
Maybe it was just too hard for you? :P
And they are both promptly stolen, because neither is inside a padlocked box. "anything sent through the mail will be stolen unless it is enclosed in a padlocked box". Anything includes padlocks and boxes. In fact, even the padlocked box would be stolen because it's not inside a padlocked box. And if it were, the outer box would just be stolen. The puzzle as written is just turtles all the way down.
The proper form of the riddle would be that anything except for a padlocked box will be stolen from the mail.
That’s why — A’s open padlock will be stolen.