(a) At any time after a claim is filed, the district director having jurisdic tion thereof may, with the prior or subsequent approval of the Director, transfer such case to the district director in another compensation district for the purpose of making an investigation, ordering medical examinations, or taking such other action as may be necessary or appropriate to further develop the claim. If, after filing a claim, the claimant moves to another compensation district, the district director may, upon request by the claimant or the employer and with the approval of the Director, transfer the case to such other compensation district.