Cable length and amperage
The misunderstanding is about the unts: the battery capacity is expressed in Ah, which means the number of Ampères that it can supply for an hour, or the number of hours fot which it can supply 1 A of current.

The cable hasn't a great influence on this, other than dissipate power due to its length. But at that low current, it shouldn't be an issue if it's big (and I bet it is!).

So, given that your current is .15 A (150 mA, rounded to the top ti be safe), the smaller battery should ideally be able to supply the camera for 4.5/.15 = 30 hours, if the values are correct. But probably the capacity will be a bit less and decrease with time, and the consumption may be higher, and you will have a slow leakage depleting the battery.

But for this scenario, 4.5 Ah seems to be enough, I guess (depending on how long he needs the camera on).

With the 7 Ah battery, the duration will be 7/.15 = 47 hours.