About shrinkwrap - Any way to apply it to a vertex group and move the rest the proportional distance? it's probably a very basic question but i have no idea how to get it and i have to say that my use of blender is quite basic.
I have this object that I want to attach to the surface of the mountain

I know that with the modifier I can join the object to the mountain, but the whole shape would be lost ... and assigning a group of vertices will only affect them, being this way:
My question is if there is any way to get the remaining vertices to move while maintaining the proportion with respect to the others, something like this:
I'm still investigating, but any help is more than welcome.
Thank you!
Edit: thanks for the answer, but the problem is that there would be hundreds of objects like this, they are simply a plane to create a forest effect
And the interesting thing would be not to lose the UV map so as not to have to map them all. In fact, being different, I could not even transfer the mapping.
Instead of a subdivided plane, use a subdivided edge like so :

Add your shrinkwrap :

Now add a Screw Modifier set to Z axis, angle 0°, with 1 step and tweak the screw value:

Moving the source object along the X Axis :

You can add a solidify modifier after all this to add thickness to your wall :