In order to participate in a securities class action, you will have to prove that you have ownership of stock related to the company in question. Doing so is relatively simple. To prove you have ownership of stock related to the company in question in a securities class action, you need only provide the confirmation slips you received when you originally purchased the stock.
In a securities class action, the confirmation slips signifying your stock purchase are important papers and should be filed with your other financial papers and documentation. If for some reason you don't have them available, however, it's possible to use brokerage statements or to get other official documentation created and printed by your brokerage firm, showing your ownership of the stock over the time period since its purchase.
A signed letter stating your ownership of stock, while it might work as legal proof of ownership in other situations, isn't ideal in a class action settlement, and if possible you should try to get more solid documentation once you know that the case is going forward.
If a securities class action lawsuit is pending, the claims administrator will be the person in charge of gathering this type of evidence from all involved parties. He or she will likely request the proof from you at the close of the class action case.
Before joining a securities class action, it is important to understand that as a member of the class, you will have very little control over the trial. The attorneys and lead plaintiffs will handle the day-to-day logistics of the case and will (along with the court) determine whether to accept a settlement or not. Of course, this also means you aren't going to be responsible for any legal fees for being a member of the class action.
If you are confused about how to prove stock ownership in order to join a securities class action, you should strongly consider speaking with a lawyer to find out what evidence will be considered sufficient.