With exceptions, most brokerage firms are required to keep documents for 6 years under Rule 17a-5. What you will probably need to is request that the broker/dealer provide an account history, which should show the acitivities and money flowing in and out of the account. Hopefully you will see references to checks drawn and deposited to a bank, where you can gather further informaiton.
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.
This is a strange question. The trustee is obligated to keep copies of relevant records and cannot just expect that the brokerage firm will store records forever. Brokerage firms ordinarily keep records like this for longer than 7 years. but ultimately the trustee has the obligation to keep appropriate records. Blaming a brokerage firm in a situation like this seems unreasonable.