You are both incorrect.
You do not take a new Bonus tile when you pass during round 6, so you cannot get any additional coins this way.
...immediately return your Bonus card and take one of the three available ones. ... (Exception: Do not take any Bonus cards in the last round of the game - round 6.) ...
However, it sounds like your friend is under the impression that Alchemists cannot use their ability at the end of the game, and this is incorrect. From the end-game scoring rules:
Finally, get Victory points for left-over resources: get 1 Victory
point per 3 Coins. (All other resources may be converted to Coins
for this purpose, see “Conversions” on page 13.)
(The Alchemists get 1 Victory point per 2 Coins.)
So you do not have to convert all your coins to VP using your ability before you pass. It is done automatically when counting up final scores. This means that if you did take a new bonus tile when you pass during round 6 (though you don't), then you would get the points for the coins that are on it.
Note that coins that have built-up on a bonus tile due to not being chosen are separate from coins that a bonus tile provides as income. You get the coins that are built-up on it when you take the bonus tile:
If there were Coins on
the newly taken Bonus card, put them on your Faction
But you only get the coins that it gives for income at the start of the following round, during the income phase.