A medal with a history

One James Baker has contacted Rouser with the following: ‘I am researching my father’s family which originates from Lewes.

‘I am not aware of any existing relatives in Lewes but my father James Frederick Baker, who was born in Rustington, West Sussex, gave me a medal which was awarded to his grandfather, James Baker, in the latter part of the 19th century by the Mayor of Lewes. The medal carries the head of Queen Victoria on one side and on the reverse the crest of the Borough of Lewes and the inscription:

“Victoria Jubilee, Presented by Alderman Farncombe, Mayor, June 20th 1887”.

‘On the edge it reads: “To James Baker for rescuing F (unclear initial?) J. Barrett from drowning”.

‘So James Baker would have been my great-grandfather and I believe his middle name was Frederick but I cannot be sure.’

Can anyone help?