Does the carbocation rearrangement in a SN1 reaction specify a change in degree? I am asked to determine whether the following process is likely to involve a carbocation rearrangement or not:


  


I think it is possible through the rearrangement given above (though the rearrangement cannot become a secondary or primary carbocation). Can someone please clarify if the carbocation rearrangement specifies a change in degree?
The most common carbocation rearrangements involve [1,2] hydride or alkyl shifts. As a typical result a secondary carbocation is converted to a more stabilized tertiary carbocation.

In the course of these reactions, the migrating group and the positive charge change place, they move to opposite directions.

This is not the case in your example. 

I fail to see how your transformation can be described as a cationic rearrangement!