While there certainly are ways to reduce or prevent tax liability on gifts such as the your father'’s stocks, you will need to speak with a qualified tax attorney, financial planner, or accountant to find out specifically what steps you can take to reduce or eliminate the tax burden that the transfer and sale of these stocks will potentially cause.
If you would like to read some more general information about IRS obligations and options available to individuals struggling with tax debt, I encourage you to visit the Bills.com IRS Debt Help page.
Inheritance and gift taxes have been progressively whittled down in recent years, so you may find that you will owe only a small amount in taxes for having received this large gift. However, if you sell the stock after having received it as a gift, I would expect that at least some amount of capital gains taxes would be due, though you may be able to structure the transfer to reduce your liability.
I do not have enough information to make any definitive determinations, and encourage you to consult with a tax professional that can take a closer look at your financial situation and determine the best way to structure the transfer and sale of these shares. I hope that you will be able to minimize your liability so that you and your sister can enjoy the full benefit of this substantial gift.
I wish you the best of luck in finding a qualified tax professional to assist you, and hope that the information I have provided helps you Find. Learn. Save.