Problem with SIM800L V2 & LM2596 step down


I'm trying to supply my SIM800L V2 module, that needs 5V and 2A, with two 18650 batteries in series and the LM2596 step down module. The problem is that the module is not working properly with that configuration, it receives and responds simple commands, but it can't make HTTP requests because of the current, I think.

With a power supply it works perfectly.

Is the LM2596 enough for SIM800L V2? I'm thinking that the LM2596 can't give enough current but I'm not sure, should I bought a ¡n step down with more output current?