One more thing to consider with external batteries is that they usually don't have 100% efficiency, more like 70-80%. I have used a outdoor tech kodiak mini (2600 mah) to recharge a cell phone with battery of 2600 mah, but it only charged the battery to 71%. From what I read on the topic, this can depend on the battery, the phone itself, and the length of the cable used to connect the battery to the phone (shorter ~6 inches being more efficient than a longer cable). Some of those things you can control, some you can't. Supposedly anker has more efficient batteries but that might also just be marketing. A higher quality, shorter cable should also make a difference (hypothetically).

TL;DR Keep in mind that if you plan on charging a battery of 10,000 mah to 100%, you'll need a battery with at least 20% more capacity (possibly more), at least 12.000mah. A 5600 mah battery would probably only provide 4500 mah of "real" charge at most.