Don't worry, it's okay! Every transaction you make online is recorded in the banking system, and the transaction records in the bank account are evidence. You can print it yourself or go to the bank counter to ask for the statement.

Answer to the supplementary question: the statement of the fund company is sent free of charge, usually once every quarter. Of course, you should write down the specific address of the communication clearly. On the customer details page of the fund website, there are generally columns on whether to send the statement (please look for it) and choose to send it.