Change material of object using geometry nodes modifier values

Question

I made a succulent generator and I want to be able to change the colors (and some other values that a material has) through the small menu of the geometry nodes modifier. I already have some inputs there, as you can see, but those are just properties of the geometry node object, not its material.

The problem is, I don't know, how to "unpack" the group input in the material in the geometry nodes setup so that I could connect it to the "group input" node there. The material has a "data type" of material and I can't find a way to set its values. I've tried connecting it to the "group input" node in the geometry nodes editor, but that only allows me to assign a different, already existing material, not to change the values of the material. Here is the node setup in the geometry nodes.

And this is my material. You can see i added the "group input" node here, too, but I can't find a way of setting those values.

How could I "add" the input variables to the geometry nodes modifier menu?

EDIT: I've tried Crantisz's solution. However, it works only on an object that has only one instance, not on my geometry nodes object, that is composed of many instances of the object. Is there any way to make it work? Here is a picture of how the node setup works on many instances (it unfortunately doesn't change the color), and another one showing the node setup:

And here it is when I apply it only on one instance of an object:

Answer 1

Set up what you want looks like this:

1. Connect (somehow) color input to color output.

if you scatter instances, they should be realized:

2. Set color output to attribute (write custom name in the field)

3. Use this attribute in the attribute node.

The group Input that you use in material is useless. Until you not group some nodes into a node group.

Answer 2

Try to use attributes that are linked to values (integers or float) in GeoNodes. Then transfer the attributes to the shader nodes and connect them.