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By 'phone backup battery' I assume you mean a USB power bank type device.
My experience with other devices with Li-On batteries is that if discharged most will come to life and the device will become functional within 3 to 5 minutes of being connected to a charger. However on occasion its taken around 30 minutes.
However assuming it has a flat battery and comes to life when connected to a charger or USB power bank that doesn't telly you that much about the battery and how well it will hold a charge. In the absence of test kit only usage will give you an answer.
One thing I'd add though and this isn't based on scientific knowledge, if the battery is completely flat once I'd got it on charge I'd want it to charge to 100% in one hit, I'd not want to put a bit of charge in, disconnect and then re-connect later to finish charging.
Good luck.
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