Wavery's suggestion is good. Progressive Dynamics makes very good converters (designed AND built in USA), but the output voltage can't be adjusted by cellphone. When you set the battery type as "Lithium", the output voltage in new models is 14.4 volts. In older models the output voltage is 14.6 volts.
Both values are higher than you want to have within long-term storage of Lithium battery packs ('LFP' , Lithium Ferro Phosphate). But a decent battery pack either pre-assembled or built form 4 individual cells at home, should include a "Battery Maintenance System" (BMS) which will manage cell balancing and limit charging to a limit you CAN change, without opening the trailer - you just hold your cellphone near your battery compartment (outside the aluminum skin) and specify a lower 'maximum charging limit voltage'.
During trips, you can use allow up to 3.60 per cell (14.4 total). That maximum must never exceed 3.65 volts, but 3.60 is already more than 99.5% full. Actual use of Tthe battery, within that last one-half of one percent, can create issues you don''nt want t0 have. So stop at 3.60, with 'balance' start slightly lower. A good PD converter will continue to offer more charging current, but the BMS will refuse to let any charging current into the battery.
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TM='06 2619 w/5K axle, 15" Maxxis "E" tires. Plumbing protector. 800 watts solar. 600AH LiFePO4 batteries, 3500 watt inverter. CR-1110 E-F/S fridge (compressor).
TV = 2007 4runner sport, with a 36 volt "power boost".
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