Upgrading from 212-1AE31-0XB0 to 1AE40

We have a machine which has 1212C 6ES7212-1AE31-0XB0 installed in it and it was programmed with TIA v11 SP2. We don't have the original program with us. My task is to upgrade the current PLC to a newer model which is 6ES7212-1AE40-0XB0 for which I will obviously have to upload the program from the currently installed PLC, somehow change the CPU to the newer model in the HW config and then download it to the newer model. To upload the program from the current PLC which was programmed in v11 I will have to use TIA v12. I will open an empty project created in v11, manually add the unspecified CPU and detect it, then copy the program blocks of the currently installed PLC from the online access option and paste in my project. Compile the project and save it. This project will now be v12. But TIA v12 doesn't have 6ES7212-1AE40-0XB0 in the HW catalog. What do i do now? I guess i will then have to open this project in v13 and then change the CPU to the newer model. Maybe v13 would have the newer model 6ES7212-1AE40-0XB0 in its HW catalog. Then compile and save and download this project to the newer model. I want to confirm from the experts that would these methods work? If yes then I'll order v13 as currently we only have v11, v12 & v16.  

There are a lot of topics about uploading projects from the PLC -> PG. Here's one example

S7-1200 6ES7 214-1HG31-0XB0 v3.0, does not support uploading to PG/PC

If you have a license fro TIA v16, you can use the same license with all prior versions of TIA, you don't need to order V13, you can just download it from SiePortal.