How to store more waveform after trigger and less before?

Yes, what you want can absolutely be achieved.

Before you capture a waveform use the horizontal position adjustment knob to change the position of the orange cursor at the top of the screen.

This first image show a capture from my scope with the horizontal position set to the center of the screen. The second image shows the same signal (but a new capture) with the trigger set close to the left side of the screen. You can see that in the second image I've captured much more of the signal.

Waveform capture with trigger in the center

Waveform capture with trigger near the left side

Annotated image of Rigol DS1104Z

I'm not familiar with your scope, but I think I've marked the correct knob. Also, there may be a setting you can change that will set the default horizontal trigger point to the left side of the screen.