You can transfer anything youd like from one institution to another without any tax consequences.
make absolutely sure you yourself keep track of your cost base on anything you transfer, as the new instituion may not keep good records of your cost base.
There are transfer fees, but depending on the amounts/value transferred
the receiving institution should re-imburse you for transfer fees. Make sure you get it back,,,dont trust them to do this without checking.
Just call them and ask these questions yourself. That the simple answer.
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