Whenever during the period of probation, a probationer goes from the judicial district in which the probationer is being supervised to another judicial district, jurisdiction over the probationer may be transferred, in the discretion of the court, from the court for the district from which the probationer goes to the court for the other district, with the concurrence of the latter court. Thereupon the court for the district to which jurisdiction is transferred shall have all power with respect to the probationer that was previously possessed by the court for the district from which the transfer is made, except that the period of probation may not be changed without the consent of the sentencing court. This process under the same conditions may be repeated whenever during the period of probation the probationer goes from the district in which the probationer is being supervised to another district.