What is the ruling on money earned from working in the field of T-shirt design, if this money was acquired by using an account obtained through fraud on websites that require a financial subscription?

A mere probability that the person inviting one to access his electronic account is not the owner of the account does not necessitate prohibiting access or forbidding earning from it. The default assumption regarding what is in the possession of a Muslim is that it belongs to him. If the status of unknown property is not known, it is as if it does not exist.