How can I quickly dry a green tree limb so that I can use the wood?

Here's some good advice on how to dry wood: https://www.wood-database.com/wood-articles/drying-wood-at-home/

If you're air drying it, you probably want to wait one year per inch of thickness. A kiln can be used to speed up drying, but kiln drying may introduce defects, such as splitting and cracking. You're probably better off just setting it somewhere dry with some ventilation and coming back to it later.

Needs to "cure" for a period of time. If you cut it into pieces, it will dry faster. Depending on how thick, 6 months to a year is standard. If you set out in the sun, like where I live where it gets super hot in summer, and turn often, might happen a bit quicker.

I agree all: Unless you split it to 1 inch Strips, you are looking at a 3 month to 6 month wait time, reliant on the inches per Split.

However, it should note, there are better uses for Quality Wood than Fuel for Burning.

If you cut them in 2" Rings your results may benefit you double by:

A. using these as part of landscape additions (such as Steppingstone Alternatives) while you instead

B. Burn Garbage Wood that avails at mostly any Fuel Pellet Suppliers.

Because: you would not use Fuel Pellets as Landscaping Alternatives, likewise you do not use Resources that are Nominally used entirely in Landscaping as a Fuel Pellet Alternative.

I myself, was happy right where the limb was in the first place...in the tree! Since it's not, I will be patient and allow it to s-l-o-w-l-y dry till next season. Gotta love Mother Nature! Thanks for every bodies help.