For heirloom, this is nearly impossible. Not a direct family member.
Think it is a war trophy because the gun werw bring back by his father
Not impossible because your uncle must be the brother of either your mother or your father and he can transfer it to them. The appropriate parent can then transfer it to you. That means that your parent has to get a RPAL including taking the safety test at a cost of (locally) around $125 for the safety course and $85 (I think) for the license. That is still probably cheaper than the hassles of rebarreling the gun. If your choice is to rebarrel, a person with a dealer's license can transport it to their facility and have a gunsmith rebarrel the action plus destroy the short barrel. The cost of that is probably going to be between $200 and $400 depending on who you select and what their rates are.
almost forgot; while in this case the gun is easily considered a war trophy, section 12(7) only requires that a gun be made before the end of hostilities. Whether or not it was ever used in war and how it arrived in Canada is unimportant.
cheers mooncoon