Green’s Dictionary of Slang

fish v.2

[SE]

to shoplift, to steal.

[US](con. 1948) G. Mandel Flee the Angry Strangers 138: In October. When you went fishing for a coat.
[UK]J. Colebrook Cross of Lassitude 101: The termites of the life [...] who ‘heel’ and ‘boost’ in stores, who extract bundles of notes from banks by means of skillful ‘fishing’.