I have used several of these no interest balance transfer cards over the years, they are very effective when paying off big debt amounts, because sometimes it gets to the point that you're paying that much interest that your monthly payments barely even touch your actual debt. These cards solve that problem in an instant. What's more once your 29months runs out, if you still have debt on the card, you can just transfer it again to a different card, effectively keeping your debt interest free.
Now I've not actually used the Halifax one, however I'm assuming that they're all pretty similar, indeed the several ones that I have used over the years all had the same process.
Now not all cards accept money transferred over from store account cards as balance transfers, so you may get charged for it. However, there are ways around this.
Sorry I've just re-read the message and noticed you said store account not a store card. Credit cards don't accept store accounts at balance transfers because they class it as a payment rather than a transfer. So yes you would get charged for this, but as I said before there are ways around this.
So first of all, apply for ANOTHER credit card, if you've just received a Halifax 29months interest free then you shouldn't have no trouble getting another card. The APR doesn't even need to be good so get any that you can, preferably one that can take the full amount from your store account.
Next pay off your full store account onto this credit card, this may take a couple of hours, I normally leave a day though. Once the payment has gone through, IMMEDIATELY transfer the whole amount onto your interest free Halifax card, leave this one a day too just to be sure, then your store account will be sitting nice and interest free on your Halifax card, saving you lots of money.