12.7 volts is not enough to charge a 12v battery. That power source would just be able to run some 12v things such as lights and fans.
It is useless for what you want to do.
BTW it does not "send 15 amps". What it does is provide that 12.7 volts. Whatever amps you get depends on how much lower the "load" is in voltage. Where the battery is the load at say 12.4 volts, the 0.3 volt difference will not make for many amps at all.
You just have to triple that $50 budget and get a proper converter. EG:
https://www.boatandrvaccessories.com/products/powermax-pm3-60lk-12-volts-60-amp-power-converter-battery-charger-w-led-light