When moved during the year, How to prorate income for the state tax returns?

Hi, My timeline:

I was living in NJ.
Graduated in April.

Start work in May ( start earning and get relocation money and sign on bonus)

MOVE to WA in July.

 

For NJ tax return, turbotax ask me about how much I earned while living in NJ. My question is:
1. For the relocation and signon bonus, should I split it like 3/7 for NJ ( because i worked for the comapy for 7 monthes last year and 3 month happened in NJ)? Or should the whole amount of relocation and signon bonus be for NJ tax return?

2. should I just report all the salary paid to me through May to July for  NJ? Or should I also prorated the July part ( as I moved and lived in WA in July)

Thank you.