the file does not reflect the formatting on my computer
Are you saying that conditional formatting is not visible ?
Any ways, I have used the below formula in conditional formatting in column F of sheet A and then selected red background when condition is met.

Formula: copy to clipboard 
=MATCH($F3,'SHEET B'!$C:$C,0)


Hope this helps.

Regards,
DILIPandey

<click on below 'star' if this helps>