Signature is not autoinserted in Notes 8.0.2

I had a user call in recently, complaining that, even though she’d defined a signature to be added automatically. She got no error message, and had not changed anything about her setup.
 
Though she hadn’t changed anything, a change had been made. All the mailfiles’ design (for those who ran version 8.*) had been upgraded to version 8.5.1. As it turned out, there was a bug in that design, meaning that signature settings did not work for people running client 8.0.2.
 
The solution here is simple, and can be one out of two; either downgrade the mailfile design to version 8.0.2, or upgrade the client to version 8.5.1.