Apple on Monday began shipping its new iPhone 3G S handsets to customers who were among the first to place their pre-orders last week following the handset’s introduction at the company’s annual developers conference.

The new iPhones, believed to be manufactured by Foxconn Electronics, are shipping out of Shenzhen, China, which is home to mainland China’s second busiest port, ranking behind only Shanghai.

Although customers provided with shipping notifications weren’t given a specific arrival date, Apple had promised delivery by this Friday, June 19th, the same day handsets go on sale nationwide at AT&T, Apple, Best Buy and Wal-Mart retail stores.

A quick check of the Apple Store appears to suggest that customers who place their pre-order today will still be eligible to receive their device on Friday. Prospective buyers should note, however, that orders placed online for new iPhones aren’t easily manipulated given that each order is tied to an AT&T account.

Customers who wish to change the model of iPhone they’ve ordered may need to wait up to two business days to resubmit their order because it may take that long for AT&T to reset accounts as being eligible for upgrade or early upgrade pricing, some people have been told.