A good place to go for questions like this is the TSA (US Transportation Security Administration; they do passenger and baggage screening at US airports). There is this handy site here:
https://apps.tsa.dhs.gov/mytsa... (as you can see from the domain, it is officially from the TSA); search for "lithium battery" and "jumper cables".
On the subject of batteries: For the past two years, the TSA (and in some cases European departure airports such as Amsterdam AMS) has required that for each battery [in hand luggage] you can show the matching device at the checkpoint and that this battery is intended for use in this device (e.g. camera batteries: you must have the matching camera with you).
Additionally, all lithium batteries belong in carry-on baggage (source: TSA, "What can I bring"), not in checked baggage.
If it helps: I bought this battery pack [1] (20,000 mAh) in the USA in February 2016 and took it with me to Switzerland in my hand luggage without any problems.
Please consider all information as non-binding - I am neither working for the TSA nor do I have any other expertise! All my information is based on personal experience.
And if I may give you a tip: if you tell the official at the security check (outbound and return flight) what you have with you, show them and explain, they are often very friendly and there are no problems.
[1]
https://www.amazon.com/gp...
