Is it permissible to assist one's sister's husband in his work as a mystery shopper to evaluate company services?

It is permissible for you to deputize for your brother-in-law in a permissible task if you will perform it as required, and if the company has no objection to it. This is because there is no harm for an employee in delegating another to perform a task if what is required is merely the execution of the work. However, if the entity stipulates his direct performance of the work, either explicitly or by custom, then your deputizing for him is not valid.