What an archaic country you find yourself wanting to stay in! If BA have cleared off the scene then I have a feeling your 'immigration department' would be the kind who wouldn't know any different if presented with a home made document produced on Photoshop so long as it had an authentic looking stamp or seal attached to it.... whatever authentic means. Not sure I'd want to put it to the test though.

Have you considered just saying this email or screenshot is all the proof BA provide. If you need more than this please contact BA yourself?