I'd let it get fully dormant for at least a week.  You'll need to wrap the roots in a wet paper towel and that in plastic.  Ship it priority and have her pot it up right away.  Water it lightly and be sure she uses a well aerated soiless mix.  She should store it between 35 and 45 degrees if she can.  Most figs can take colder but since you don't know about this one that's a pretty safe range.

Hi Paul,
I would keep it and send it beginning march.
If you touch the roots now, the tree might wake up and it will be hard to handle.
I lost 3 I had inside my flat last year - I thought I would help them grow faster - I will never do it again.
I had 2 sister-trees inground and one showed some figlets this year already...
So my 5 cents : keep the tree untouched for now and send it in march  when the recipient will have an easier task at taking care of the tree.
One question : how is the climate in Massachussets ? Don't you have an adapted cultivar for ouside in that climate ?

Of course you could be lucky with a warm spell too.

That's pretty cool that it's a family heirloom!  If you have to send, obviously check the weather.  I know we're having a warm spell in Albany NY the next few days.  Also, if you send and she pots it up, I would store in a safe protected part of the attached garage.  Behind something or tucked in a corner where the winds won't freeze it if she opens the garage for any amount of time.  Also you can put a piece of wood or something under it to insulate the roots from the cold concrete.  Finally, she can try calling the post office and ask them to hold it there for pickup.  Sometimes they'll accomadate that.  What i did recently because the temps were in the teens and i had cuttings coming, I put a note at the mailbox and on the door asking usps to leave the packages inside the garage door because th contents will get damaged by the cold.  worked great!
Timothy

If you can keep the tree dormant until March, you can send it bare root.  It may do better sent in a pot with soil, but nurseries send bare root trees all the time.

Ship it in soil (which will better protect the roots from cold) and ship it only temps along the shipping track are above freezing for the whole trip. If your sister doesn't know much about plants, then having here deal with a bareroot plant is one more way for something to go wrong.

I agree with everything Jon wrote. Since I expect that by the time the weather conditions between you and Mass. will have temps above freezing along the entire route, that tree will have broken dormancy. I would consider cutting the tree back to no more than a foot tall once it's gone dormant and then attempt to keep it dormant for as long as possible. Maybe at that height you can find room in a small/spare refrigerator set to around 40 degrees. You'll have to protect it against dessication in the fridge. Even if refrigeration isn't an option, the smaller, presumably actively growing tree should be easier to handle and should withstand any delays along the way better than a larger tree with more leaf surface area.

Just wanted to thank you all for the advice. I appreciate that there are some differing points of view; Gives me plenty to consider.

By the way, since the time that I first posted this, about half of my trees have dropped about half of their leaves, while the rest are still completely green and have all of their leaves.