If you establish a 403(b) account under the school's 403(b) plan, you may roll the Traditional IRA assets to the 403(b) account. As you may know, the rollover from the Traditional IRA to the 403(b) cannot include after-tax amounts or amounts representing required minimum distributions. You should check with the 403(b) provider and the IRA custodian/trustee to determine whether they require special paperwork to complete the transaction.
Generally, because current law prohibits the rollover of after-tax assets from IRAs to regular 403(b) plans, you are not allowed to roll your Roth IRA assets to the 403(b) plan. However, if your employer has adopted the deemed IRA provision for its 403(b) plan, then you may be able to rollover your Roth IRA assets to the deemed IRA under the 403(b) plan. To be sure, check with your employer.
This question was answered by Denise Appleby