Best Powerbank with integrated Lightning cable

My GF really doesn't want to deal with a separate wire in her bag, and her old 3000mAh Powerbank with integrated Lightning cable only has around 2000mAh capacity left and is in general too big for what it is.

Googling gives me some options but just wondering if anyone has experience with any specific model out there.
I think something with a capacity of up to 5000mAh would be a good compromise between portability and usefulness.

Thanks in advance!

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