Hi Eric,
Its always growing season in Costa Rica? You are giving me a bad case of ''climate zone envy''. We had our first significant snow. It is mostly melting, but got over an inch.
The link to John G's videos, that he gave you should really help you. John is a great azalea grower, his videos are fantastic.
Okay, looking at the photos. If it were mine, I would repot it right away, as Anthony said, put it in a perlite-peat moss blend. I would use more perlite than peat, say 2/3rds perlite, 1/3rd peat. I sift the perlite over a window screen to eliminate fines. I am able to get a fairly coarse grade of perlite. Sift the peat also. In the end, for both, more will go through the screen than stay on top, add the fine stuff to your growing bed for vegetables.
At home I use a blend of Kanuma and perlite, but I know you can't get Kanuma or pumice easily. So use peat moss.
I would pot this into a large diameter but shallow pot, say 15 inches by only 4 or 5 inches deep.
Don't chop it now. Let the growth it has force it to make a large root system. Then either 6 months or a year from now, do the trunk shop. It should be bushy with hundreds of leaves before you do the chop. That way it will explode with back budding. If you chop now, with the weak root system, you may not get much in the way of back budding.
I would assume the azalea is a hybrid with one of the more tropical azalea species in its background, like Rhododendron simsii. So I'll assume it will handle your warm climate. After it settles in, you will get a feel for when it is putting out spring like growth. You will have to adjust from John's videos the timing of what you do, but his videos should really help you.
Nice find.