How to project UVs form the big object to the small one to display part of the image that is behind it as shown in the snapshot below.
I think the simplest way to do this is to join the two planes into a single mesh. Then position the viewport to be perfectly perpendicular to the planes, enter Edit mode and UV Unwrap from View. Then when you apply the image to the material using UV texture coordinates they will align perfectly. You can then separate the meshes and they will keep their UV layouts.
In order to accomodate the skew of the mesh, the uv layouts must be edited concurrently. Here's how to do that.
- Join the two meshes. Unwrap with project from view.
- In the UV editor select all and size to 90% of the uv grid area.
- Turn on UVs>Constrain to Image Bounds, and Enable Proportional Editing in 2D mode.
- With all vertices selected move the vertex group to the lower left corner. Then in turn, with a fairly large proportional range selected, pull each of the other 3 corners towards each corner of the uv area. If your proportional edit range is large enough, the edits to the large mesh will affect the small mesh.
- Once done, leave Edit mode and check the alignment on the meshes. The two meshes can be separated at this point.
Denis shared his alternative which used the Shear command (CTRLSHIFTALTS) to tilt the vertices instead of using proportional edit. This was a great solution for this specific mesh issue.
Here is more convenient way to do so: You need UV mapped object as source and another object with the same texture but any mesh data with assigned UV map as target. For target add DataTransfer modifier, select source object, enable Face Corner Data transfer as Nearest Face Interpolated and below click UVs as face corner data layers to transfer.
The result quality depends on target mesh density.