When working at the Science Museum in the 1980s, I was asked to call at the head offices of Ealing Electro-Optics plc, in Watford, to discuss their archives of old Beck documents. The outcome was that I was allowed temporarily to take away for photocopying their earliest sales books, and was given microfilm of their later similar records. This was on the understanding that I myself answer requests for information sent to the company by those wanting dates for instruments supplied in the past, and this I have done until now. I also presented a summary of the material in my Notes on Modern Microscope Manufacturers, published by the Quekett Microscopical Club in 1996: reference should certainly be made to this book in addition to any notes below.
To put the dates into context, notes on the history of the Beck firm are required:
Smith & Beck was the successor company to James Smith, essentially a maker of mathematical instruments, but who made J J Listerís famous 1826 microscope for Charles Tulley [died 1830]. Smith then began to specialize in such instruments, and set up shop for himself in 1839 with the assistance of Lister, at 50 Ironmonger Row, Old Street, London.
In 1847 James Smith took as a partner Richard Beck [1827-1866], nephew of J J Lister, whereupon the firm was called Smith & Beck, of 6 Coleman Street in London. Catalogues from 1848 to 1865 exist, and show that the microscopes were well designed, but only part of the wide overall trade.
In 1857 Joseph Beck [1829-1891] was made a partner, and the firm, at the same address, was renamed Smith, Beck & Beck.
In 1865 Smith retired [to die in 1870], and the name became R & J Beck.
Reference should be made to M Shephard  - The Beck microscope family, Quekett Journal of Microscopy, 39, 577-594.