It's been explained several times in this thread, but maybe a photo reference will help.

So my question should be: How do i close “that connection” on the motherboard?
Could you please explain to me how do to do that?

The jack shorts out the ground and "switch" pin when it is in circuit. When you remove it, you reopen that connection and need to close it again on the motherboard if you remove the headphone board.

But I don’t have the headphone’s board anymore, so I can turn the on/off. I guess that I need another solution, if there’s one.

See Kitsch's or Alley Beach's replay above.

Hey guys, I’m having the same problem. I had a broken headphone board, so I ripped all the cables that connects the headphone board on the main board.. now I got no sound from the speaker. Can someone please help me on that?

Don't forget http://thursdaycustoms.bigcartel.com/product/dmg-audio ! They aren't available with headphone jacks installed right now, but it's a nice little space saving thing that keeps the DMG looking stock.

beautiful.  that did  the trick. I figured it would require some kind of jumper,  just didn't know where  without you guys.

yea, just ground the white wire. the reason the prosound still works is its bypassing the amp. the amp reads the digital input and chooses whether the speaker stays on or off

Oops, yah I was totally wrong, I completely forgot about the switch. Sorry about that

you can just add a jumper to ground the speaker again if you remove the headphone PCB.  try attaching where the white wire was to ground.  i *think* the white wire is the post-switch speaker wire at least, perhaps that isn't right.  memory

removing this PCB basically removes the switch that engages the speaker.  you've got to switch it back on again somehow.  a jumper should do the trick.  or a bit of hook up wire if you want it insulated

the switch in the jack is a grounding switch.

I guess I assumed they were related since my speaker  went out immediately following removal of that pcb,  but my rca  pro sound still works. I must have inadvertently did something else in there.  I'll check again.

If you make the new prosound jack pre pot then you can turn down the speaker with the volume pot like normal and still hear the jack. The bad thing is there will be no volume control when using headphones.

Well, it is - in a way. There's a switch in the headphone jack which turns the speaker on and off. But I think it should be always on if you cut all the wires.

Here is the gameboy scheme, the switch is in the bottom right corner (of the first picture).

AFAIK the speaker is not dependent on the jack PCB.