These exist, just look for inverter/chargers. Tripp-Lite APS750 as an example though may not be LiFePO4 compatible. I use one as a sump pump power backup. Vari

These exist, just look for inverter/chargers. Tripp-Lite APS750 as an example though may not be LiFePO4 compatible. I use one as a sump pump power backup. Various Victron products as another example that are actually LiFePO4 compatible: MultiPlus, Quattro, or others depending on what capabilities you need.