Will 2016+ 18" wheels be ok on a 2011 CX-9 in regard to TPMS?

My mom currently has a 2011 FWD CX-9. She recently moved to an area where it snows and is planning on replacing her 2011 CX-9 with the newest generation next year. I am going to use my yearly bonus check to buy snow tires and wheels for her as it will make her more comfortable driving in the winter weather. I know the 2016+ wheels will fit fine but what about the TPMS? I understand there are sensors. Are the sensors the compatible between a 2011 and a 2016+ CX-9?

Should I just have the shop swap her sensors from the 20" All-Seasons this year and then buy an additional set for the newer model when she buys that?

Thank you for your help.

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