How exactly will dual listing affect the OZ SP

As now the image is more clear, this thread is to try to understand the mechanics of the dual listing and how it will affect the price of ASX:IHL

so now Incannex will issue a number of new shares lets say 5M new shares, these will be offered to investors in USA as part of the IPO. Roth will be the bookkeeper of these new 5 Million shares.

Once trading starts in US, on the first day, will Roth only have 5 M shares to offer to investors ? what is the mechanism of transferring the over 1B share from the Australian market to the US market ?
In other words, how can Australian investors benefit from the demand in US ?

Thanks,