This is the first time I've invested in a fund such as this, so I apologize if this is a stupid question - as the current investments have been made via semi-anonymous "user IDs" on BTCT, how will you know how to tie an investment to the same person on a new exchange?
It's a good question. The exchange emails all issuers with a list of current participants in their assets. A new exchange would provide some means of importing that list, such that old numbers would match up with new ones.
Although I've just said in an earlier note that I have no intention to suspend trading in the fund, in the case of a transfer to a new exchange, we would announce a
planned suspension of trading -- and
not a surprise one coming out of the blue "for your own good" -- so that we could secure a current participant list. With that list in hand, we could then begin a move to a different exchange.
EDIT: Whoops, I should have paid more attention to that notice saying the thread had been updated while I was typing, as it looks like Rannasha has already done a good job of covering this.
I know that BitFunder has some option to recover/import shares already. On the account page, there's an option to "claim shares", where in my case it says that no shares were found linked to my email address (which is true) and there's an option to fill in a different email address to claim shares from (presumably it will send some verification code to that email address to verify ownership). I don't know if Havelock has a similar feature.