Question
Is it possible to transplant fruit trees that are 15-20 years old?

Answer
Deciduous trees may be planted either in the spring or the fall. Deciduous plants may be moved in the spring as soon as the frost is out of the ground, up until the time when new foliage is partly unfurled. In the fall, they may be planted once the leaves start to turn color up until the ground freezes.

When you want to dig up a tree  for transplanting, retain as much of the root system as possible.

Older deciduous trees  can be successfully moved only if a ball of soil is left around the roots. The exposed roots should be protected with moist burlap or newspaper or with polyethylene sheeting. Every effort should be made to reduce root exposure to wind and sun, keeping the ball as moist as possible. It's best to prepare the hole before digging up the tree you wish to move.

Size of the root ball and size of the hole:

For deciduous trees and shrubs the soil ball should be:

Width = 9-12 in. in diameter/every 1 in. of tree diameter
Depth = 6 in./every 1 in. of tree diameter

For example: A tree trunk 2 inches wide would need a soil ball of 18-24 inches wide and 12 inches deep.

Dig the new hole twice the size of the rootball and as deep and fill with good top soil and mulch around the tree with not more than 3 inches deep of organic mulch and water good.

This will be a large rootball for the tree you described and may take special equipment to move it. One of these machines is called a Vermeer tree spade. Here is a web link to their page and dealer locations.
http://www.vermeer.com/vcom/EnvironmentalEquipment/Line.jsp?PrdlnID=3840