Why does my Wemos D1 Mini stops working while charging via solar?
The TP4056 Module will output a max of 4.2V which is less than the 5V the Wemos D1 Mini is expecting on its 5V connection (Assuming you have connected the circuit as shown in the Github guide). When the solar panel is charging it's likely that the TP4056 is causing a driving issue on the supply of the Wemos causing it to potentially Brownout .
I would not connect the solar panel to the Wemos like this, I would have it connected to the battery then the battery connected to a 5V Step Up Power Converter like shown below (This reduces efficiency but give the MCU a stable supply),

My recommendation for the wiring,