Laptop monitor problem. Tell me about the wired connections

On my toshiba laptop, I like to hook it up to a large monitor when I can. Unfortunately, I recently snapped the internal plug off… Now that’s over with.

It looks too difficult to solder back on. However, there is a white connector which connects the laptop’s monitor to the motherboard. Would it be in any way possible to solder the wires from the plug to a full-screen monitor cable?

Are they wires which have the ability to be extended by soldering longer wires to themselves?