Correct power supply

Hi, im using a sim800l module (EVB) and the power suppply are 4 x 1,2V nimH AAA Baterreies (700mAh) in series (makes 5V). The module works fine but when i try to transmit data the module powers down. After some research i founded that the module sometimes as 2Amp peaks wich i think is the problem. How can i fix it ? is there any component (like a capacitor) that i can use or should i use a diferent kind of batteries ? it always need to be AAA type.

If you taking more than the Batteries can give then it will not work. NiMh and NiCads have a lowish C rating for a prolonged time.

LiFe batteries are an option as are LiPo and have a higher C rating. Both of these types need a dedicated charger

GSM modules are designed specifically to work from a single LiPo cell as in a mobile phone.

LiFePO4 might work, but their voltage is lower, note. AAA NiMH are not going to handle the
high current peaks, yes ~2A is quite normal, the average will normally be a lot less.