Having calculated the shared secret and blinded the public keys using it, she then send Bob the ecash token, including the ephemeral PUBLIC KEY (E) that she created.
Discussion
Now Bob can use the magic of ECDH... he takes his private key (p) and the ephemeral public key that Alice sent with the ecash (E), and he can calculate the SAME shared secret!
He can now use that shared secret to derive a private key to unlock the ecash.
The beauty of P2BK is that it provides perfect privacy. Alice and Bob do not need to communicate at all to set it up - all Alice needs is Bob's public key.
The ecash is locked to totally unique blinded public key(s), keeping the receiver's identity private from anyone who views the ecash. This means tokens can be published securely in public.
The sender's identity is also protected, because Alice uses an ephemeral keypair to create the shared secret, and throws it away afterwards. All Bob needs is the ephemeral Public Key!
You can read the draft specification for NUT-26 here:
https://github.com/cashubtc/nuts/pull/300
You can also play with P2BK (though don't be reckless).
P2BK Lock Tokens with Cashu NutLock:
https://nostrly.com/cashu-nutlock/
P2BK Unlock Tokens with Cashu Witness:
https://nostrly.com/cashu-witness/
or Cashu Redeem: