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there is no tax on inventory, however there are sales tax on goods sold.
As the Company A holds inventory in Texas and if any goods are sold and shipped to the customer in Texas - that transaction is a subject for the sale taxes in Texas because the Company A is actually doing business in Texas.
If the Company A uses facilities of the Company B to store an inventory - that will not provide any difference in sales tax allocation.
Based of your clarification that is the Company B that actually sells goods are required to collect sales tax if selling to customers in Texas.
The Company A would sell goods to the Company B and as long as the Company A doesn't have any business presence in Texas - it is not required to collect any Texas sales tax.
For qualified businesses investing in Enterprise Zones, Texas offers a one-time state sales tax refund, a one-time franchise tax refund and preference for all programs administered by the State of Texas - that may be an opportunity for the Company B if it qualified.