Rate of Laptop Battery Charging
You're not actually charging your laptop battery with the solar system battery. (At least, you shouldn't be.) Your laptop includes charging circuits to make sure your battery gets the voltages and currents to charge it properly. So long as those circuits are fed with voltage and current within their operating range, your laptop shouldn't care what the exact nature of the source is. AC line and switching converter, charged battery, discharged battery, all that's going to matter are voltage and current capacity.

Of course, there are a lot of details to "voltage and current capacity" that might bite you, this is a gross oversimplification, your mileage may vary, professional driver on a closed course, American Express cards not accepted.