Customs in Virgin Islands (British)
The Customs department is located in Road Town on Tortola, which is the largest island in the British Virgin Islands. That being said, there are Customs posts spread throughout the inhabited islands which will check your shipments and your person as they come to the country. They are fairly efficient, given they get a large amount of travelers there every year and given that they are located so close to the US Virgin Islands, particularly St. Thomas and St. John's. In fact, there are Customs officials positioned at all the ferry terminals in the British Virgin Islands because ferries go between the two countries multiple times a day.
Security concerns when shipping to Virgin Islands (British)
The only real concern you should have over safety when shipping to the British Virgin Islands will be when talking about some episodes of piracy in the Caribbean in the past. The British Virgin Islands, as well as other island nations in the region, have multiple security measures in place to combat such behaviors, but that does not stop these law breakers from doing their deeds overall. With this in mind, it would be a good idea to get some insurance on your items before you ship them there, although these types of occurrences do not happen all that often.
Shipping destinations in Virgin Islands (British)
The British Virgin Islands is actually a cluster of over fifty islands and cays. The four main islands, Tortola, Virgin Gorda, Jost Van Dyke and Anegada, are the most populated and receive shipping services. Fifteen of the islands are not inhabited, such as Salt Island, so there would be reason to ship there. Other islands may only have one or two residents on them so they may need to travel to a more densely populated island, like Tortola, to pick up their parcels. You will want to check with your shipping company for detailed information on what the recipient should do in order to get their items so that you can notify them before you ship.