How to export Blender file so it can be opened with the textures on another machine? Basically, my client wants to open the Blender file I'm working on but every time I send him the blender file he manually has to connect the textures with the objects. 

Is there any way he can just simply open the .blender file with everything ready to go?
You can pack all textures into blend file from menu: File > External Data > Pack All Into .blend
Then save file and it should work.