Controlled Battery Charging using Arduino

I have found a 1A LITHIUM BATTERY MODULE which needs either a USB or voltage input of 4.5-5.5 V in order to charge the battery.

My project will consist of the module being connected to the Arduino, and the Arduino will feed the voltage input to the module. I need it that way because I have to control the charging state.

For example, I need it to charge for a specific number of hours, then stop the charging, which is possible because of the code I will be using.

My concern is that will the module damage the Arduino if that is the case? And also, will a simple digitalWrite HIGH code is applicable in order to feed the module with the input voltage?

Thanks for your guidance.

Your question makes no sense.
How will the module be connected to the Arduino?
An Arduino cannot supply 1 amp to anything.

My goal in using the module is the LED indicator which turns to green when the battery is fully charged, and red when it is still charging. Is there a way to imitate this function using Arduino only or is there another device that is suitable for my purpose? Thanks

If you're asking if Arduino can turn the device on and off, sure you could use a transistor and let Arduino turn it on and off but you can't power that or anything even close to that directly off of an Arduino.

Why not just use the charger as is? What is the actual problem you are trying to solve here?