It's not stored. It's applied to the raw Bayer data, every time, before demosaicing. Same with noise reduction.

What you can store, is metadata that informs these "first step" filters, like lens data, and maybe other sensor readings.

One of the advantages to proprietary data storage, is that you can have company-proprietary filters, that produce a "signature" effect. Third-party filters may get close to it (and may actually get "better" results), but it won't be the same, and won't look like what you see in the viewfinder.