Your power supply is about (13.8x3) 41 watts and will probably do a 40 watt job thru the charger. If you limit youir power usage to the 40 watts or a little less then it should be ok.

An easy example is a 3S lipo at 3 amps. (12.5 volts x 3 amps= 37.5 watts) Your battery may or may not be able to handle 3 amps and if by chance it is smaller than 3S3000 mah then you got it made . If it is bigger then perhaps it can be charged using somethng less than 3 amps and will just take longer.