Finniss is building for delivery of first production by the end of the year, with the project on the fast-track to opening thanks to its major project status.
As part of the contract CSI is designing a crusher circuit for Finniss, with run-of-mine ore to be stockpiled before being fed into the crusher.
The crushed ore will then be sent to the site's dense media separation plant and turned into spodumene concentrate for export.
Crusher civil works are nearing completion, with CSI expected to mobilise to site in June.
Core managing director Stephen Biggins said the award of the crushing contract was another significant step in the development of the Finniss lithium project.
"Core staff have done a great job getting the site ready for CSI to start work next month," he said.