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Please allow me to assist...
There are some issues to consider.
The LLC is a business structure allowed by state statute. For federal tax
purposes - depending on elections made by the LLC and the number of members, the IRS will treat an LLC as either a corporation, partnership, or as part of the LLC’s owner’s tax return (a “disregarded entity”).
In your case if the LLC is owned solely by the BVI company - as a single member LLC - it is disregarded entity - means ignored for income tax
purposes - with income and expenses are reported on the owner's income tax return.
Because the owner is a foreign entity (nonresident alien) - it is taxed ONLY on income from US sources. There are complex rules
for determining the source of income - you may take a look into IRS publication 519 - www.irs.gov/pub/irs-pdf/p519.pdf
See page 12 - Table 2-1. Summary of Source Rules for Income of Nonresident Aliens.
Specifically for your situation - Business income realized from the Sale of inventory which was purchased is sourced Where sold.
Thus income from selling goods to US customers is classified as income from US sources and if goods are sold to customers outside the US - it is NOT from US sources.
Because the LLC is a disregarded entity - income is reported by the BVI company - assuming it is a corporation - it must be registered with the IRS (EIN should be obtained) and as a foreign corporation should file from 1120F - www.irs.gov/pub/irs-pdf/f1120f.pdf
Again - only income from US sources must be reported.
There is no special business license unless goods that you are selling are require one - for instance if you are selling medical equipment, drugs, firearms or other regulated goods.
You may register the LLC in any state. Most popular states for such purposes are Wyoming, Nevada and Delaware.
You may use any mailing address - including the address in California. You may use any US or foreign address, PO box or address forwarding service. However it is possible that California taxing authorities
would assume that you run business out of California - and will try to assess state tax liability. Because California taxes are relatively high and dealing with taxing authorities might be a complex matter - I would avoid that.
Sales taxes are regulated by states - not by the federal government. There are two aspects fro online sales - sale transactions
are subject of sales tax based on the customer address. However the seller is only required to collect sales tax if the seller has a nexus in this specific state. Thus - for instance - if your business is not physically presented in California - you are not required to collect California sales tax, but the buyer would be required to pay corresponding use tax
If the LLC will regularly use the 3rd party fulfillment center located in any specific state - that will be classified as having a nexus in this state - and the LLC will be required to register in this state and collect sales taxes from customers located within that state.
Please be aware that while the LLC is disregarded entity for income tax purposes - it is a separate entity for other purposes - in particular - for sales tax purposes the registration would be in the name of the LLC.
For instance - if the LLC is originally registered in Nevada, but will regularly use the fulfillment center in California - that LLC should be registered as a foreign (out of state) LLC in California. It will be required to pay California franchise tax
(minimum $800), will be required to collect sales tax from sales to California customers and remit that amount to FTB. In additional - the solo owner of the LLS - which is your BVI company will be taxable on income from California sources.
In other words - business activities would be under California jurisdiction.
Please let me know if you need any clarification of help with other tax related issues.