Cables do matter. Different ones can only handle different currents.
The thicker ones can handle more.
Just give it a try yourself. Use some old thin cable and use the 2a transformer and the charging speed is limited
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I agree that SOME cables cannot handle 2.1A charging current, but I submit that virtually every one *I* own can, and I'm, frankly, pretty fast and loose when it comes to choosing a cable when I need one for charging.
BUT, just to be sure, I broke out my three-year-old Re-TraK self-retracting cable which uses extra thin (and I mean THIN, like 24 gauge or higher) wire. This particular unit has been abused, and has several knots in the cable, and won't retract any more. Plugged it into the Samsung charger, and right away I read 1800mA charge current, which is as high as I've ever seen, even with the Sammy charger and the shipped USB3 cable.
Point is, I think it's WAY more likely that the charger block/car-plug is not powerful enough OR is not outputting its advertised current. (The other option is, of course, that the charging control in his phone is defective, which should be rectified). There was an article about a year ago, and if I can find it I'll repost, but the conclusion was basically that, after being bench-tested, none of the 3rd party chargers on the market can meet their rated output, and some fell FAR short, in the neighborhood of 50%.
Use the factory charger and cable, and if your charge is slow, go get the phone swapped. If it's normal rate (~1% up per minute), and your other charger/cable is not doing the same, then kick your other charger to the curb.
Mark