1. I have a 11.1V/4.4Ah lithium battery, whose full charge voltage is at 12.6V

2. there is separate 12.6V/5A adapter in the instrument where we need to fit the battery.

3. Goal is that if mains is not availabel, system switches to battery & if main is present, it both charger battery with 1.5A & supply current to load also.

4. Adpater is not itself current limiting, so it will send over current to battery, what is right way to limit current in battery so that it wont take more than 1.5A for charge.

 

Hi,

A current regulator is best. If you can assume some voltage levels then a power resistor will work too.

 

Unless you want a fire, get a properly designed multi cell Li-Ion charger. You need to monitor the voltage on each cell in the battery and control both the charging and discharging.
Although there is plenty of info on line to show you how, it is not a trivial thing to do.