Be careful- Li Ion battery needs a special charging regulator which can be bought with the particular cell phone only. If you try to build yours, you can destroy the battery quite fast.
I would best check if your phone DC power supply really is 5.0 V, 0.8 A. It means that it has an internal charging regulator and then you can safely use ANY 5V, 0.8 A DC power supply.
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From 12 V car power you can use a 7805 voltage regulator to get 5.0 V, up to 1.0 A. Include a 1 A fuse in the output.