General principle is to ensure both controllers are running the same version of ONTAP. For the FAS3250/FAS3140, both support ONTAP 8.1.2 through 8.2.5. Upgrade the FAS3140 if needed to make it match.
Then swap network cables, SAS and FC cables, and reassign disk ownership. This document outlines the process for moving from a FAS20xx to a FAS31xx - the process of "using the FAS20xx root volume" is essentially what you want to follow - https://library.netapp.com/ecmdocs/ECMP1140585/html/index.html
If your system uses LUNs over FC or iSCSI, please ensure you follow the directions about saving LUN serial numbers and reserialising on the new system. I don't think it will be necessary in your scenario, but you should be prepared and verify this is the case.
As the other poster said, raise any case against the newer system, which is hopefully under support, and it will be fine.