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Once you transfer a stock from one account to another a deemed disposition occurs..That means that you either have a capital gain...loss..or it is revenue neutral..meaning you transfer it at what you bought it for..
yOu can do this with out selling it but the gains and losses rules still apply..that is all that they are telling you..so you will have to pay or claim on that transfer.You can do what Hap suggested but the stock movement will only effect the account that the deemed disposition is coming out of ..the new account has no capital losses or gains benefits so won't matter on that end.