Establishes "Welcome Home Veterans Bonus" program in DMVA.

New Jersey's A5045 bill establishes a "Welcome Home Veterans Bonus" program within the Department of Military and Veterans Affairs to encourage veterans to remain in the state after military service. It provides $1,000 for veterans who served outside the continental U.S. with hostile fire pay, $500 for other service (overseas or domestic), and $300 for certain expeditionary service, with eligibility requiring service in specified operations (e.g., Operation Enduring Freedom), an honorable discharge or discharge related to sexual orientation/gender identity/HIV status, and six months of New Jersey residency before entering service. Veterans who die during active duty receive a $1,000 payment to heirs, and applications are processed through the DMVA with established evaluation criteria and an appeals board. The program is funded by a dedicated state fund and requires applicants to submit documentation verifying residency and service.