Yes, but unless you have experience with soldering, I don't recommend you try it. Instead find a electronics shop or friend that has experience in soldering small items.
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If you insist on doing it yourself, buy; Perfboard, De-soldering braid, Thin rosin core solder, no clean flux pen, spool of wire the size of what your soldering and finally a soldering iron with a tip small enough to match what your working on.
Practice:
- Soldering the spool of wire you bought to the perfboard.
- Removing solder from the perfboard with the braid.
- Tinning the tips of wire and then re-heating it to attach it to the perfboard.
- Search YouTube for soldering tutorials.
Once you feel comfortable:
- Disconnect the battery.
- Clean any old solder off the pads of the Motherboard and the connectors of the speaker jack with the braid.
- Use the flux pen on the pads of the motherboard and jack.
- Tin the pads on the motherboard.
- Re-attach the jack.
- Check to make sure you didn't accidently short anything by accidently soldering 2 pads together.
Note: Depending on how badly you messed up the jack, it may be necessary to solder the wires directly to the board.