Welcome to San Diego! I'm in Ocean Beach, love it down here
From their website: http://www.fns.usda.gov/wic/howtoapply/whogetswicandhowtoapply.htm#Moving
WIC participants who move from one area or State to another are placed at the top of a waiting list when they move and are also served first when the WIC agency can serve more individuals. WIC participants who move can continue to receive WIC benefits until their certification period expires as long as there is proof that the individual received WIC benefits in another area or State. Before a participant moves, they should tell the WIC office. In most cases, WIC staff will give the participant a special card which proves that the individual participated in the WIC Program. When the individual moves, they can call the new WIC office
for an appointment and take the special card to the WIC appointment in the new area or State.