Need Help with Earbud repair

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Hello everyone,
I am new to this forum as well as audiophile itself so please bear with me. I have a pair of V-Moda earbuds w/mic that fell victim to the common "earbud sound loss" in one ear. I've decided to fix them myself for they will not honor a warranty due to me purchasing from an unauthorized seller. I narrowed my failure at the junction where the 2 earbud wires (1 from each ear) meet to make 1 thicker wire down to the jack. I also decided to replace the jack with one from Switchcraft due to many folks reporting of failures there. My question to the community is: Can I just solder (the two wires from ear buds and one from headphone jack) together at a three-way union and just heat shrink the overall joint? Also there are two tabs that are on the Switchcraft, where do I put the wires to solder and which wire/and tab is ground? Do I simply solder the ground wire to the fatter tab and twist the other two wires together and solder them together at one point on the other tab? I am trying to gather as much info as I can before I go screwing things up and end up spending more money. Thanks everyone.
 
Stereo plugs are TRS (tip ring sleeve) the tip and ring are left and right (can't remember which is which - do a search), and the sleeve is ground. The head phone wires wiill have a center conductor and a conductor around that which serves as a ground. both outer conductors go to the sleeve and the inner conductors go to the tip or ring.
 
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