the crossed arrows with a crown above and a v below were used from 1813 to 1855. Also still used 1855 to 1868 and still used 1868 to 1875. But you can narrow it down closer than that. Percussion rapidly went out of "fashion" after central fire cartridge became the norm with breach loading guns. Call it early 1860's at the latest.

Quick records I could find:
John Probin, gunmaker, principle place: Birmingham, Warwickshire 1799
Note of Defamation recorded in Lichfield Record Office B/C/5/1799/74

Will of John Probin, Gun Maker of Birmingham , Warwickshire 2 August 1800 Prob 11/1346 He is too early.

The Birmingham Proof House was established in 1813 which your gun has post 1813 proof marks. There has to be another, perhaps a son or another relation because Steve Barnett has a hammer double from "J. Probin" listed for sale and it is a 1860-1870 period gun, a very early breech loader by style and features Like Jones under-lever, wedge/key fore end. But the timeline is in question for a son. Perhaps born 1780's-1800 might still be in business as late as 1860 but still could have started several to many years earlier. I would be looking for information on the later J Probin in the time line area of 1840-1870 at the latest.

Sometimes the research is as much fun as anything else.