It's not that simple. Because your old employer and your new one are two unrelated companies (right?), you'll have to stop the current plan and start another. Yes you can continue to pay to Eagle Star if you're happy with them, but it will be a new plan. When the new one is established, you can transfer your benefits from old plan into new plan. That has implications for vesting periods.
If you're happy with the IFG service, you can stay with them. Make sure you know exactly what they'll charge you for setting up the new plan. Or ask one of the brokers that post here on Askaboutmoney.com for a quote.