You are assuming wrong. The UK tax inheritance based on the deceased - that amount is paid as the Aunt is UK domiciled (assuming they are!) Your wife may still owe more tax in ROI - depending on how big the Aunts estate actually is. Under Irish CAT, your wife is inheriting approx €60k in Cat band C, so 20k is tax free and 40k taxed at 33%- so €13,200. (If she's already had some band C inheritance in the past this will be different depending on amount, but for here, I'm assuming this is her first)
I think the below is correct - if anyone thinks i'm wrong please shout!
The UK double taxation treaty (see revenue website) allows for some of the inheritance tax paid on your wife's portion of the estate to count towards this 13200 liability. It may not cover the full €13200 though due to the tax free threshold on UK estates. Was the aunt married? If not I think that's £325k. So for example if she left an estate of £500k then inheritance tax of 40% of 175k was paid by the estate (£70k) leaving 430k to be distributed to beneficiaries. Your wife gets £50k which is 50/430ths of this - so 'She' has paid 50/430ths of the UK inheritance tax already ie (50/430*70k) £8140 (€9768) leaving the balance (€13200-€9768) to be due once the process is followed on my account/ROS.
If the estate was worth more than €700k then your wife could well not owe any more tax but still needs to declare to revenue.