If I transfer my FID using recovery, what happens to my farlet? Is it controlled by the new FID private key?

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lemon3

How this works, for anyone who has not studied the details.
https://paragraph.com/@purplesubmarine/farcaster-account-recovery

So, Farcaster can use the recovery function to transfer my fid (and my wallet) to a new set of keys that I don't control?

I’m pretty sure that farlet is registered as a key associated with the fid like other signers so nothing changes