FBO is a industry-wide, accepted term by all IRA custodians. It helps maintain the administration chain for an IRA along with the asset ownership: the person for who's benefit the custodian holds the money.
FBO is used in self-directed, inherited, education and transfer IRA structures. The custodian will always be listed first, with the person who is entitled to the assets designated after FBO.
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When trustee-to-trustee transfers are made, the checks issued are made payable to your new trustee FBO. This is unlike a rollover, where you are able cash the check because it is made payable to you.
The significance of the FBO designation lies with the IRS. Money movements and transfers made through an FBO do not generate a 1099-R and therefore don't generate taxes.
Do not confuse all FBO designations as IRA accounts. An FBO may be utilized in a trust or charitable contribution designation as well.