Not at work, that poor spider. Thats a reportable accident under health and safety at work regs (injury to spiders section). You'll have to do a full investigation, review your risk assessments and safe systems of work and produce an action plan to ensure spider safety during fork truck operations. There will be safety committe meetings, with tea and ginger nuts, to attend and enough paperwork to justify additional temporary staff. Most of all you need to ensure that you you cannot be held responsible as the relatives of the spider will seek compensation. It could cost an arm and seven legs.
* I have too much time on my hands sometimes.