Is it permissible to continue pursuing the recovery of one's rights from the workplace after its ownership has been transferred to the sponsor's brother and the sponsor has refused to transfer the sponsorship, or must one cease doing so?

It is not permissible to take one's right from someone other than the oppressor, based on the Almighty's saying: "And every soul earns not [consequences] except upon itself, and no bearer of burdens will bear the burden of another." The oppressed person should refer their case to the court or to whomever can grant them justice.