The component you identify as missing, the third one from the top of the connector, is FL2400, a 120 Ohm / 210mA Ferrite Bead. It is on the gas gauge line between the battery and the Tigris chip. This part is easy to order from DigiKey or scavenge from a donor board. This chip is pretty common across multiple models of iDevices so just check a schematic to find another one. Alternatively, you could just short the two pads. The ferrite beads acts as a noise filter on the line so while it is preferable to have it, shorting it will at least allow your phone to work. If you ever see erratic behaviour on your gas gauge, then you would need to replace it properly.
These components are tiny, measuring just 0.5mil X 1mil and it is in close proximity to the battery connector and stuck next to a shield. This is by no means an easy repair unless you have good tools and some experience working at this scale. Whatever you do, don't just assume you can use a standard soldering iron otherwise you risk damaging your logic board even further. There are plenty of videos on youtube that make it look easy but these folks are using multi-thousand dollar micro-soldering workstations under stereoscopic magnification.
If you don't feel comfortable doing this yourself, then look for a repair shop that does micro-soldering repairs. It shouldn't be a very expensive repair.
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