The answer is false. The interest parity condition states that if there is no country-specific risk the forward discount on a currency will equal the excess of the home nominal interest rate over the foreign nominal interest rate. Barring risk considerations, therefore, the country with a consistently higher inflation rate also tend to have consistently higher nominal interest rates. But this says nothing about the difference between the countries' real interest rates. Real interest rates will differ because of country-specific risk, foreign exchange risk, and any expectation that the country's real exchange rate will change in the future. Inflation differences will not be a factor in real interest rate differentials.
When the differences in the inflation rates between countries are large, say in the order of 5 to 10 percent, it is unlikely that risk premia together with expected real exchange rate appreciation of the currency of the high nominal interest rate country will be large enough to reverse the effects on nominal interest rates of the difference in the inflation rates. Of course, temporary differences in the inflation rates will not necessarily lead to differences in expected inflation rates and will not show up in nominal interest rate differentials at all.