My friend has a Ledger wallet, and she wants to transfer the Bitcoin from a ledger wallet to a different ledger wallet (without a record of the transaction).
Is this possible in a SAFE way?
This is possible only if you import your seed words from first ledger device to second ledger device, there will be no transaction and you will have full control on both devices.
Keep in mind that coins are always on blockchain and not actually on hardware devices but importing seed words on multiple devices you can lose all your coins, and you are reducing your security, so do this only if you are the owner of both devices.
Transactions for coins like Bitcoin are public and everyone can see them, but using coinjoins with Wasabi wallet or bitcoin mixers like Chipmixer will increase your privacy a lot but, there will still be some transaction history for receiving address.