First and foremost, please do not allow your partner to travel to Hong Kong. He would be prevented from leaving HK by HK Immigration.
It seems as though the company who employed him in Hong Kong has reported his salary to the iRD in Hong Kong. That's the only way the iRD would know about it. The company may well be obliged to report his salary to the iRD, I don't know. Your partner's salary would probably be considered as income earned in Hong Kong, unless the company he worked for had a UK office. Any income earned in a country is taxable in that country. Naturally the HMRC would tell your partner that he needed to pay tax in the UK, since that is where he is living and he would be considered to be a resident of the UK for taxation purposes.
So, the bad news is what is known as "double taxation". Which means that tax is payable on income in his home country as well as where the income is earned. Now, there used to be an arrangement between various countries which recognised tax paid in one country as absolving the employee from paying tax in the other country, however I am not sure whether HK (SAR) China and the UK have such an arrangement and only a tax professional / lawyer would be able to know for sure.
It may be that if he can provide evidence that tax has already been paid in the UK on the income he earned from the HK company, that the iRD in HK will waive any taxation obligation to HK. However, I must reiterate, he must not travel to HK to sort this out (or for any other reason) or else he will be denied exit (until it is resolved to the satisfaction of the iRD).