PC replaced by doppelganger

[Zweisteine]

I've been running the Lost Mine of Phandelver with a group of kids, and have recently run into a fairly serious problem.

In Cragmaw Castle, there is a doppelganger (in drow form), who is supposed to fight to the death, and not surrender/get captured. And the players grappled it very successfully. Then they left it, the unconscious Gundren Rockseeker, and one PC in the room while the rest of the party went to clear out the last few rooms.

The PC left alone with the prisoner tried to interrogate/torture it, and it faked being unconscious. The PC then went to tie it to a chair, but needed rope, so decided to untie it and then retie it. At this point, I sent the other players out of the room.

Naturally, as soon as it was untied, the doppelganger bludgeoned the PC into unconsciousness (in the first round). It then killed Gundren, destroyed the hidden map, and took on the guise of the PC.

The players returned (after they finished clearing the castle) and the doppelganger told them that the drow prisoner had escaped sand knocked him out.

and went through one last short battle before the session ended.

Pre-post Edit:
While typing this post, I came up with a clear solution. I just fix the situation a bit by saying the doppelgänger ran away, and the cover story it gave as a PC is the real story. This also makes more sense time-wise, as the doppelganger would not have had time to change clothes.
But I still think this is a good question. If I keep DMing, this seems like a useful situation to be able to deal with.

[TrexPushups]

Depends on the group.

If you have players that are mature/capable enough to handle it letting the player play the doppleganger until discovered and giving them bonus xp for their character when they resume can be a fun option.

[Toadkiller]

If you could have a way for the PC to survive (the drow is in a hurry and only thinks he's dead) I, as a player, would go along with it.

The player gets to be a villian for a few " episodes" and then gets their character back. Could be great fun.

[Daishain]

Let the PC act as the doppleganger for a bit, and work with him in playing a believable doublecross. Have him roll up a new character, and introduce it in a manner that helps offset the loss. The doppleganger, if still alive, comes back under your control after that.

[RedMage125]

For future reference, it is possible to do this. I ran Age of Worms back in 3.5e, and one of those modules calls for the replacement of one PC by a doppelganger. What I did was talk to that PC and let him know. he continued to play his character, even using the same sheet (since he was a barbarian I told him to limit his use of Rage). I gave his actual character the XP for the encounters that the doppelganger was there for, no sense in punishing his character.

When the PCs infiltrate the doppelganger stronghold, they find a room with a bunch of people tied up, they all look like the whole party. At the point, the player resumed control of his actual character (who was the only one genuinely tied up), and the doppelgangers (including the one in the party) attacked.

[Knaight]

I'd generally hand this off to the player, at least on the logistical side of it. Maybe get a brief overview of what they're doing with the actual character, then reintroduce them at an opportune time.

[Maxilian]

Depends on the group.

If you have players that are mature/capable enough to handle it letting the player play the doppleganger until discovered and giving them bonus xp for their character when they resume can be a fun option.

I was thinking about these, is a really nice idea and could be really fun