Hello, my husband and I moved to Italy

Your husband can have a home in Italy, but not residence - he is tax and legally resident in the UK.  He needs to 'emigrate' immediately.   As it standshe should be filling in an Italian tax return adn paying Italian tax on his worldwide patrimony and deducting what he pays in the UK under the double tax agreement.  This is not financially a good idea to put it mildly

It is quite possible to be registered at the Anagraph office in the local commune as a resident in that commune (indeed it is a legal requirement if you are in Italy for a period of more than three consecutive months). Whilst registration as a resident may be taken as indicating residence in Italy for tax purposes it is not necessarily the case that you would be tax resident in Italy. So far as a tax residence is concerned, it is possible in the first instance to be tax resident in both the UK and Italy. However under the UK/Italy double tax agreement it is only possible to be tax resident in one country. Whilst the question of tax residence is a matter of fact, and therefore depends on the particular facts of each individual case, from the information you have posted it would appear to be that your husband is tax resident in the UK and non-tax resident in Italy. As such he would be liable for UK tax on his worldwide income with double tax relief been granted for any overseas income which suffered tax in the country of source. In Italy he would be liable for tax on any income arising in Italy. It is essential that as much documentary evidence be retained supporting the position and your accountant should be able to advise you what to keep (I would suggest as a minimum copies of all travel arrangements and credit card receipts showing where used as these can assist in verifying presence in the UK). At some stage the Italian Tax Authorities may enquire and will no doubt take some persuading. Whether having registered as resident at the local commune and your circumstances change so that you are no longer required to be registered (e.g. you are only spending short periods at a time in Italy) requires you to take action I cannot comment on. The main impact seems to be on registering a car, the rates applying for IMU/Tarsu and health service benefits.

Thank you for both replies, and yes it seems that he should give up his residence in italy and re register when he is no longer employed in the UK.