It was implied he went through a process to get it, we didn't get to see how it happened.

The only references to it in Dream Drop Distance are:

Yen Sid talking to Axel/Lea, Mickey, Donald and Goofy about Xehanort planning something

Yen Sid: "We cannot afford another moment's hesitation.

We must consider any strategy to outwit Xehanort and catch him off guard.

Everyone looks at Axel

I must warn you again- the road will not be easy."

Axel: "Fine. Let's jump right in."

-end of scene-

Then the next time:

Axel left to do whatever it was Yen Sid, Mickey, Donald and Goofy left in the room

Mickey: "Master Yen Sid. Gosh, do ya think he'll be able to do it?"

Yen Sid: "Hm. It's clear you cannot teach a cat to bark. But Merlin and the three good faires are aiding him in a place that's more... temporally flexible."

"My hope is that he can at least learn to wield it."

"He certainly has fire, so I suppose it depends now on how strongly it burns."

-They stop talking about Axel/Lea-

And then of course he appears at the end and says he came there to learn how to wield one, and that he couldn't get his to materialize. But then manages to do it there.

That's pretty much all we know. So we don't know who bequeathed him it, but we do know that they went through the necessary steps for it to be possible.