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Can't help with the initials TJW except to say a very similar mark was registered at both the Chester & London offices by Thomas J Watson but he is described as a dressing case fittings manufacturer.
The case was assayed at Birmingham in 1890.
Philip T. Priestley's "Watch Case Makers of England" shows that mark being entered at Birmingham on May 12, 1887 by Thomas Webb, 4 Craven Street, Chapel Fields, Coventry.