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Looks like there's a little solder left on the - pad. If you're lucky, it will be good enough to do some testing with. I've marked it on the image in blue.
I've selected a few probe points as potential candidates:

Can you check continuity between:
1. Point 2 and point 1.
2. Point 3 (tin on the bottom of the black part) and point 1.
3. Point 4 (tin on the top of the beige/white part) and point 1.
You will need a multimeter for this of course. Either measure continuity using the continuity tester, or test for ~0Ω resistance. If any of these points provide continuity - great! You can solder the speaker wire to said point, though perhaps you may need to use a thinner wire to bridge the current one (because it's massive compared to the components). |
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