Yes, the basis of CUSIP B will be CUSIP A original price plus any broker charges you may have incurred.
"The basis of stocks or bonds you buy is generally the purchase price plus any costs of purchase, such as commissions and recording or transfer fees. If you get stocks or bonds other than by purchase, your basis is usually determined by the fair market value (FMV) or the previous owner's adjusted basis of the stock.
You must adjust the basis of stocks for certain events that occur after purchase."
Publication 551 (12/2022), Basis of Assets
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