If your home state requires you to have a permit to possess a handgun and that handgun has to be registered than it would be unlawful for you to have it period. More than likely you would have to turn it over to authorities or to someone who has a federal firearms license to hold it for you until you've met all the legal requirements of your home state. This should have been done at the time the handgun was left to you. However every state's laws are different. I don't know if it would be a good idea to contact authorities at this time. They could possibly arrest you for the illegal possession of a handgun. Being that you are in Massachusetts, a state that is notoriously hostile towards the 2nd Amendment. It might be a better idea to contact a lawyer before you proceed any further.
You may be on slightly stronger grounds if the pistol was left to you through a Will. (easier to prove you are the current owner). As Desertman suggested, I would contact an attorney in your state familiar with firearms who could offer guidance through/around the pertinent laws there.
I would not ask Law enforcement, as if there's a problem, they might legally have to act on it.
In most states, if something (even a deadly, evil handgun) was left to you formally, in a will or other bequest (including a witnessed oral statement), then that thing already belongs to you, and need not be "transferred." Ask the family lawyer who handled the will (or other disposition of property) for guidance.
Since the item probably already belongs to you, it would be absolutely legal to ship it by FedEx or UPS to yourself, from yourself, assuming that the item is legal to possess in your own state of residence.
The "from yourself" part can legally be handled by anyone in your father-in-law's state whom you choose to nominate for the job. They would just label the package as if you, yourself were sending it to yourself.
How do I know?
Some years ago, a really good friend left me a pistol by witnessed, verbal bequest. I asked his widow to send it to me. When it arrived, it was evident that the gun did not fall under the permission-slip that my CRFFL represented, so I wrote a letter to BATFE asking for advice and clarification.
A nice BATFE Agent quickly replied that the situation was a non-issue, and unrelated to any FFL, because the gun had been left me by bequest. Thus it already belonged to me, the widow was merely acting as my shipping agent, and federal law permits anybody to ship his own gun from any location to any other location, so long as receipt of it is legal at both ends of the shipment.
I can quote chapter and verse after a little research, but since the laws in question are easily found on-line, I leave it to you to do that for yourself.
BUT... If you and the deceased both live/lived in Massachusetts, you're probably screwed.