NY is an independent so the NY DOR is going to get detailed w2 info... and NY DOR does best job of any taxing authority in electronically tracking and cross matching $$.  If you leave off the 414H..... they gonna know.....

414H is taxable in both NY & NJ (and yeah... even though it's the spouses NJ 414h plan... they're filing MFJ and PS is correct to have it show up on the IT203...

you'll get most of it back in the NJ COJ .... the reality is that it's not a perfect world and not worth the letter from the NY DOR in a year or so...  

... another fine example of NY and NJ Departments peeing across the river at each other.  (check out the new NY convenience of employer rule to see the latest in the cross Hudson tax contest).