I went the other way - Italy to Ireland - unfortunately the Italian system does'nt even allow for the reclaim of tax paid under your tax credits/personal allowances etc as they only grant such credits on a pro-rata system!!
As for reclaiming amounts paid under their 'prsi', again that was not reclaimable (hopefully I'm entitled to a state pension, should be good for 2 years of work!!) as apparently EU had just changed making it apparently transferreable to other member countries but not reclaimable. That may be your best bet, if you can transfer the PRSI paid here to your Italian fund. Buon fortuno e lavoro!!