Use a boost converter to make the higher voltage.
This also allows you to control how much current is getting dumped onto the batteries. These kind of batteries need to be carefully monitored while charging and discharging if you want to get full capacity and long lifetime. A microcontroller directly controlling the switch of the boost converter is probably the electrically simplest way to achieve that.
There should also be a way to measure the voltage of each cell separately, and optional current shunts around each cell. The micro watches the voltage of each cell, and performs cell balancing by enabling the current shunts across any cells above the average voltage, then shut down charging altogether when the cells reach the maximum safe voltage. The micro can control the charging current since it is controlling the switch of the boost converter. It can either measure the current and perform control that adjusts the PWM duty cycle to get the desired current, or it can compute the current open loop by knowing the voltages and the inductance.