Distribution of stock

I have an acct with a measly 122 shares of stock. I was ordered in our ED to transfer half of those shares to my ex.
He was instructed to open a stock acct and give me the details so that I could have the shares transferred to him.
Our ED was ordered over 3 yrs ago and he still has not opened an account nor given me details.

Is there some statute of limitations at which point I could sell those shares or transfer them to a new account as I now need to close that stock account.

No. You have an obligation to comply with the order and if you do not transfer them, you could be found in contempt. If you have to close the account, keep the same stock in a different account until he contacts you to provide you with the information.