I am relocating my warehouse in a few months and looking for suggestions of the most efficient way to transfer inventory and be able to ship out orders at the same time.

Move the slowest moving items to the new warehouse first. Deliver the fast movers out of the old warehouse., while moving the rest of the inventory to the new warehouse.
Once in the new warehouse keep the fast movers in the center of the warehouse and store all the slow movers in the higher shelves and far from the center of the warehouse. I’m assuming all computer and phones are in the center of the warehouse.

In the absence of any other information, I’d think that @Tropical_Willie‘s advice is sound. But that might be moderated depending upon:
– the specific product/s that you stock and ship from the warehouse;
– the number of individual shipments in and out of the warehouse per day;
– how long you’ll be able to have (or required to have) both facilities open;
– staffing, machinery and automation considerations;
– security, traffic, supervisory and other considerations;
– the location of the facility and weather conditions prevailing (i.e., heating or cooling issues);
– the budget that you have to work with.

It could be that “the most efficient way” (depending on the various considerations above, and others that I haven’t even thought of yet), might be to simply close the old facility except for the movers preparing and loading the goods for storage in the new facility, and do all shipping and receiving at the new facility, or doing the move overnight or over a weekend, even if it requires hiring a temporary crew – and paying overtime to the existing staff – to work through a weekend and some evenings to do the move all at once. (You didn’t ask for “the cheapest way”, after all.)