The interest on the E bonds, as you noted, was deferred until the H Bonds were cashed. At that point you must report and pay tax on the E bond interest that was deferred.
During the interim period from the time of H bond ownership until they are cashed, the interest earned (and disbursed) is reported and taxed each year. This interest is not being taxed when they are cashed in. There should be no double taxation in your mother's situation.
Q&As from the Treasury site show the actions and the deferred amount to claim in the year of redemption. In the redemption year you will have the deferred interest and the interest earned during that year.
What if the HH Bond includes deferred interest?
With an HH Bond, you may be postponing (deferring) interest that an earlier bond earned.
How can an HH Bond have deferred interest?
HH Bonds were available in exchange for other bonds (such as, Series E or EE bonds) that had been bought earlier. HH Bonds with issue dates of November 1982 and later were only available in exchange for other bonds that had been bought earlier.
Rules that governed these exchanges allowed the HH Bond owner to wait to get the interest earned by the earlier bonds – and, therefore, to postpone (defer) paying tax on that interest – until the HH Bond's life ended – either because it was redeemed or it was 30 years old.
With the exchange, Treasury allowed the older bonds' interest to continue to be deferred for federal income tax reporting purposes as part of owning an HH Bond.
How do I know if my HH Bond has deferred interest?
The amount of the deferred interest is included in the face amount of the HH Bond and is shown in a tax-deferral legend on the front of the bond.
If the exchange included more than one HH Bond, the amount of the deferred interest was divided proportionately among the HH Bonds.
