Now we all know:

Who do you call ?...
them 'Ghost Busters' ?...
no, no..., just call Jimmy.

When I want to move trees in the spring I root prune them in the fall and add bio plex or Superthrive. This encourages new smaller roots to start growing closer to the trunk. In the spring I dig a trench around the root ball and bio plex again. Let that absorb for two or three days and then finish your dig. A tree that big I would wrap in burlap and throw in a wire basket. You can burlap and wrap in chicken wire bound tight for the same effect. Wrap it very well before you try to lift it out of the hole. A 2" tree will weigh about 150 lbs. A 6" tree is well over 1000 lbs. You can google the correct size root ball based on the actual caliper. A double truck is only calipered on the largest trunk. (Don't double it). This sounds like a very large tree and the rental of some equipment may not be a bad idea. P.S. I've been a landscaper and Landscape Designer for over 20 years. I've never moved a fig tree that big but the theory should apply.

does the fruit lose theres sweetness and taste after the tree reaches a certain age?
the reason why I want to keep it is , I want to keep growing it and get a really fat tree,
will the taste improve or starting to die down?

Looks like you can get 2 trees out of that...  Take a look at this...

http://aubreypub.typepad.com/weblog/2010/02/mobile-fig-tree.html

George: That is a very nice tree. It is a double-trunk tree which represents the twin sisters. Please let them stay together, do not separate them; moreover, the tree will weaken more further if you do divide them. The bark of your tree is like your skin. When it’s damaged, pathogens get in which cause infections easily and furthermore, your tree will devote all its energy to healing instead of growing. Thank you.

Best,
Tam

I can totally understand wanting to keep the tree as is. A lot will depend on how bound the roots are in the yard. 
From a tree friend of mine
(Remember that transplanting causes stress, which you want to minimize as much as possible. If you want to transplant in spring, it must be done after the ground has thawed and before the plant has started to bud out.  If you wish to transplant in the fall, it should occur after leaf drop but before the ground freezes. A transplant will likely not survive if it has budded out in the spring or if it has not had time to become established in the fall prior to ground freeze.) 
Fig can be very resilient and given enough care can go through a great deal, just make sure you have it's new home good to go so it, spends as little time out as possible. I moved three 15'-20' tall crape myrtles and  they had been pushed out of the ground by an earth mover.... they are lovely trees 9 years later. 
You will need to do major pruning and if you did have some cutting left over after everyone else got some I'd like a couple.

That is a huge tree!
I hope that you are not planning to transplant as is.
If so, you will need to bring in some heavy artillery.

George: Fig trees are  in the genus Ficus, from the family Moraceae. They are one of the ancient trees.   If they are healthy, they do live very long time, more than 1000, 2000, 3000 years old. Thank you.

Best,
Tam

Is the tree in Astoria?
We go there a couple time a month for seafood
I'd like to maybe snip a few twigs and get an early start if that might be possible?

Wouldn't hurt to give a tree guy a call and see about the cost of moving it...
I used to live in Astoria.... where do you go for Seafood Rich?

George
Whatever happens eventually, take a lot of cuttings and root a couple of them as suggested by someone. That will be an insurance in case it is found to be too much to dig and move.

George, any chance I can acquire some clippings too :) I'll provide an address if you provide a PayPal email.

Hi George:

You have a PM. Can you please contact me?

Thank you,

Leon

Hi George:
I finally got your PM. Look for my reply today.
Leon