foreign client

First Question:  Tax Status in Canada:  That depends.  What were your client's intentions when he move to Cyprus?  When you filed his 2014 return, did you specify that he immigrated to Cyprus and the immigration date, thus letting CRA know that he will no longer be filing Canadian taxes?  If not, why?  Was the client's intention to return to Canada?  Or, does the client continue to be a Canadian citizen and only living in Cyprus for work, under a work permit?  Does your client consider himself an emigrant to Cyprus, having established citizenship in that country?

Lots of unanswered questions that need answering to fully understand your client's situation.  

Secondly, you mentioned that the client has Rental Property in Canada.  As such, he needs to file taxes in Canada yearly to claim his rental income (or net loss) on this property.  So it makes sense that CRA has requested these tax returns.  The question becomes, what type of return is required.  If your client continues to be a Canadian Citizen while living in Cyprus all these years, then he should be filing a normal T1 tax return.  In this scenario, he would file the T776 to claim his rental income / expenses, and he would report his World Income, and then claim a Foreign Tax Credit on the tax he pays in Cyprus (on his Cyprus tax return) to prevent double taxation.  You will have to check to see if there is a tax treaty with Cyprus that discusses Foreign Tax Credits to verify if he is entitled to claiming this tax credit to prevent double taxation.  
If he immigrated to Cyprus and is no longer a Canadian citizen as of 2014, you should probably submit a paper adjustment of his 2014 return indicating his exit date from Canada.  In this scenario, he would file a Part XIII tax return as a foreigner, claiming his Rental Income / Expenses on the T776.  
Further to this scenario, CRA imposes strict requirements on foreigners owning rental property in Canada.  They are REQUIRED to have an NR4 account with CRA and submit 25% of their monthly rental income to CRA EACH MONTH.  Then they can file a Part XIII tax return to claim their expenses and receive a refund.  Or, they can apply for a NR6 account with CRA which allows them to only pay the NET monthly amount (Monthly Income minus Monthly Expenses) to CRA each month, however some property management companies don't support using NR6 accounts because of liability issues).  

As a foreigner, there are HUGE penalties for filing these returns late.  As such, you will want write CRA a letter requesting a PRIORITY ASSESSMENT for these late returns from 2015 to 2019, expressing your client's situation that they weren't aware of their requirements to file these returns, and asking CRA to waive any penalties associated with this assessment.  You will have to submit ALL the returns at one time with this Priority Assessment, as they will only offer this penalty forgiveness ONCE.  

I hope this is helpful.  I wish you well in assisting your client with this. 

Last year, I assisted a client in Dubai in filing Part XIII tax returns from 2013 to 2019.  CRA is very slow in processing these.  It took 11 months for them to finally process their 2019 return, and then they worked backwards, taking about 2 to 3 months for each additional return going backwards.  To date, they have only processed the returns from 2016 to 2019.  The 2013 to 2015 returns that were included with the Priority Assessment filing are still showing as unreceived on CRA's Representative website.  They finally just processed the 2020 return this week.  Luckily my client had Net Losses for all years from 2013 to 2018, and only owed on her 2019 which was filed on time.  2020's return also had a Net Loss.  When my client paid her 2019 tax bill, CRA placed it in the wrong account, and thus her bill remained unpaid.  It took a phone call from me to enquire about the payment before they moved it to the right account and clear up her account.  No interest or penalties have been charged to date for my client.  So she's extremely appreciative of the work that I did on her behalf.