The class action has been certified to proceed as a class action.. The class was notified of that and given an opportunity to opt-out. The failure to opt-out by the deadline only means that any settlement or verdict (very unlikely that it will ever go to trial since class actions are almost always resolved because the potential liability is so huge) will be binding on the class member. Opting out would simply allow the class membet to bring their own action, something that would never make sense in this situation because so little money is involved for any class member who doesn't own tons of stock.
The action arises out of the alleged failure by Pfe to disclose knowledge about Celebrex risks prior to and following the Vioxx injuries (Merck's somewhat similar drug) becoming public.
The only time a class member has to do something is after the case is settled, If that occurs -- my guess is it will in 12-18 months as these matters normally go -- the class member has to file a proof of claim in order to receive anything. Another notice will be sent well in advance of the deadline for doing that. It will be necessary to attach the confirmation or brokerage statement showing the purchase and price. If the stock was sold, info of the sale may be required as well, depending on how the settlement treats shareholders who still own the purchased stock vs, those who don't.
So the answer to your question is that your mother need do nothing now, assuming as is almost certainly the case, that she is willing to agree to be bound by any resolution or judgment in the class action. The notice she received has the years during which class members had to buy Pfe. I don't have it handy, but I believe that she qualifies. She may want to check the notice to be sure that the class period includes 2001.