This falls under the SWT-AWT interoperability issue.
So it demands a parallel implementation of Xembed Protocol by SWT, which is already done by AWT.

To Reproduce This:

i) Run the attached code.
(This requires swtlibraries as well as SWT
ii)An SWT Shell Comes up.
One SWT Button will have a Accelerator/Shortcut/Mnemonic Set and one Swing Button will Have a Mnemonic set.
SWT Mnemonic Will Work, while Swing one will not work.