Is a son's selling his mother's shares without her knowledge, followed by her death without her finding out, considered a betrayal of trust, and what is the ruling on purchasing alternative shares with the intention of waqf as expiation for that?

It is obligatory to safeguard trusts and return them to their rightful owners, as Allah Almighty says: "Indeed, Allah commands you to render trusts to whom they are due." Your handling of the trust without its owner's permission is a wrongdoing, and you are liable for it to her heirs after her death. You must repent to Allah. Purchasing shares with the intention of waqf (endowment) is a good deed if the company's activity is permissible, but this does not absolve you from returning rights to their owners.