I believe the P.B mark on your watch was used by the Platnauer Brothers, Birmingham, England. They had marks entered both in Chester and Birmingham. Philip T. Priestley's book "Watch Case Makers of England" has them listed as jewelers and watchmakers.
Not sure of the first names of the Platnauer brothers, have seen conflicting information on this.
Don't know if there is any relationship with the modern jewelry manufacturer R. Platnauer Ltd. located in Birmingham.
The last Chester mark listed in my book for Platnauer Brothers was entered on August 28, 1883, so the time frame is right.
Regards,
Pat.