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From the research I’ve tried to find, yes, the brokerages must transfer real shares. If they didn’t really have them but marked your account as having them, they have to go out to the market to buy them. This could cause a slight delay in the transfer since they have to go out and purchase them.
Back when a lot of people were transferring out of PFOF brokerages like Robinhood and Webull, there was a lot of talk about how it could help drive the share price up with brokerages going out and purchasing shares, so that could have contributed to some of the spikes we saw too.