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.
Mazda CX-9 Grand Touring 2016
The current tire pressure sensor resides in the valve stem. The tire shop will install the sensors when they mount the tires. I don't know what system the 2011 uses. If it is the system with the sensors in the valve stem, the batteries fail after a few years. If they swap the sensors they'll charge you for a kit with the rubber seal plus labor. No real point in the swap.
2010 CX-9 GT
You are probably ok. The previous generation has the sensors in the valve stem. The new ones do too (aside from the 2016 which used a different system to determine if a tire was underinflated).

If you buy wheels and tires, the shop will install TPMS sensors in them. At this point, I would not reuse the ones in the 2011 because they have batteries that last 10 years or so. I looked at TPMS sensors online and It looks like the aftermarket sensors that are available work on both the 2011 and 2017 and up models.
I would install the most recent tpms. Worst case it won’t be compatible with the older cx-9 but from what you are saying she won’t keep it for very long. I don’t have tpms sensors on my 2018 cx-9 winter wheels and all it does is that the tire pressure warning light is on in the dash.