Garmish, Germany to Swarvoski Krystal in Wattens, Austria

You can take the train from Garmisch to Fritzens-Wattens. You will change trains in Innsbruck. Here is the website for where you can look at timetables and buy tickets.
https://www.bahn.com/en

Fritzens-Wattens to Pertisau has a few choices. Here is a link to the Rome to Rio response to my query.
https://www.rome2rio.com/map/Fritzens-Wattens/Pertisau

Keep in mind that from the Fritzens-Wattens train station it is about a 20 minute walk to the Swarovski Kristallwelten. There is an option to book a shuttle from the train station. Another option is to take the shuttle bus from Innsbruck, which will take you directly to the Swarovski Kristallwelten. You can find all this information on the website:

https://kristallwelten.swarovski.com/Content.Node/wattens/Directions.en.html

My sister (who is a huge Swarovski fan) and I plan to visit next month from Innsbruck.

If you opt to walk from the Fritzens-Wattens train station, you should email Swarovski Kristallwelten for walking directions. They sent me a map and said the quickest way was using the bike path and then take a shortcut through their employee parking lot.

Search for the best connections here: https://www.oebb.at/en/
(from "Garmisch-Partenkirchen" to "Wattens Kristallwelten", and from "Wattens Kristallwelten" to "Pertisau")

There is a direct train (S6 or RB6) from Garmisch-Partenkirchen to Innsbruck (8:02am, 10:02am, etc.), and then you have a bus (#4125) to the Kristallwelten. Total travel time is about 2:20 hours.

Going to the train station Fritzens-Wattens is not the best idea, as the shuttle service is not operated on weekends, and walking is a bit far.
The Swarovski shuttle bus from Innsbruck is not only expensive, but also you have to wait about one hour for the bus after arriving by train.

Going from the Kristallwelten to Pertisau is straightforward by bus, but you have to change three times (travel time about 1:30 hours).