Maybe sort of.
The pk-encrypted-sk packet in PGP (see rfc4880 5.1) normally contains the 64-bit 'long' keyid of the recipient's key; this is intended to help the recipient use the correct decryption key if they have more than one, and to help the recipient identify which tag-1 packet (if any) is for them in a message encrypted to multiple recipients. It may be suppressed by substituting zero if desired.
This can be displayed by any number of PGP analysis/debugging tools, including
If Bob is accused only of a mistake, not of cheating on or lying about sending the message, and did not use GnuPG's
--hidden-recipient or similar, this is probably sufficient. If Bob is accused of (even contributory) malfeasance it might help if when the message was sent (or at least prior to any dispute) he signed it, had it timestamped by a TSA, or both, but you'd have to be more specific about the case or range of possible cases to be handled. (ObSecStack: what's your threat model?)
Assuming the key blob is still available or can be obtained e.g. from a keyserver, this almost 'proves' what key Bob used. It is presently difficult, but not impossible, to generate a false key (second-preimage) for a long keyid. (It is easy for 32-bit 'short' keyids often used for manual selection or 'verification', see https://evil32.com .) It is practical to generate collisions for 64-bit, but that would require Alice to knowingly collude in a false claim; see above about threat model.
However, that does not constitute proof the key used was (or still is) Alice's -- it is quite possible that Bob did in fact make a mistake. What reason or evidence did he use in choosing that key to encrypt to?
Just having a key with Alice's name in it is NOT proof it is her key -- those are trivial to fake.
Having a key with Alice's name in it that was signed by trusted other parties is better evidence, but not absolute -- with enough effort someone could have posed as Alice to get a fake key signed.
Even if Alice actually gave Bob this key, can he prove (1) she did so and (2) he at all times thereafter maintained it on device(s) or storage that no one else could have tampered with?
Note: similar to Is it possible to prove which public key was used to encrypt a message? which covers a broader range than just PGP.
Can I check who can decrypt my GPG message after I encrypt it?
What information is leaked from an OpenPGP encrypted file?
Can all the (other) recepients of a PGP encrypted message be identified?
which I didn't see earlier.