Assistance: Conditional formatting comparison between two FILES.

Apologies, I had to first comb through and remove any information deemed sensitive as I am using copies for learning purposes. Uploaded in original post.

I will reiterate the situation:

Sheet1: Column A: lists contractors. Rows Contain Months of the year.

Sheet 2: Same items, but many more values in Contractor List.

Months between the two sheets are common.
**Some** Contractor names will be common.

The values that will need conditional formatting will be those values in the middle, intersecting months and contractor name.

How would I get Contractor Names List from Sheet1 to be compared to those in Sheet2, then the values in their respective rows need to be compared with conditional formatting? So basically as it is set up in the attached document. The example has the yellow numbers highlighted. If say I had another sheet similar to this one in another file, is it possible to achieve it?