Replacement of a service panel.
Wires are long enough, the sheathing is cut too short to enter the box.
Can this be corrected with the use of Heat shrink wrap?
This doesn’t specifically answer your question, but it will offer the information needed to make a knowledgeable decision, based upon the insulator (jacket) compounds and characteristics. http://www.usawire-cable.com/pdfs/WIRE%20KNOWLEDGE.pdf
Enjoy! 
Theoretically, yes. As long as the “heat shrink” insulates to the same degree as the conductor sheathing. However, you would need to remove the conductor from the lug in order to apply the heat shrink. At that point, you may as well just trim the conductor. No?
Agree, thus the information contained in the link posted. 
Due to original wire layout and the design of the new box. the location of the box is being moved 3 inches to the right.
While the wires are still long enough the sheathing will not be able to enter the box.
As an alternative to installing a junction box, or pulling new leads. the thought process was that Heat Shrink should work.
Checking with the AHJ Monday.
what’s wrong, dont have any duct tape? 
I would imagine an extended 3" conduit would do the trick. William may be able to explain this better.
The sheathing MUST enter the panel no less than 1/4 inch.
Got a code reference?
110.3(b)
I guessed that you would say that. 