Convert camera frustrum to UV coordinate on texture?

You could use Camera.getWorldDirection() to get the view direction and then use raycaster to find out the intersection point on your sphere. To be clear, the origin of the raycaster’s ray would be the camera’s position in world space, the direction of course the mentioned camera’s view direction.

An intersection points always contains the uv coordinates of the intersected geometry. You can access it like so:

const intersects = raycaster.intersectObject( object );

if ( intersects.length > 0 ) {

    const intersection = intersects[ 0 ];
    console.log( intersection.uv );

}