However, their plans have hit a brick wall after INZ declined Malla's visitor visa application.
INZ acting border and visa operations manager Jock Gilray said Malla did not provide sufficient evidence to demonstrate that she met requirements for the visa.
"She did not provide sufficient evidence to demonstrate strong employment or financial commitments in her home or residing country and did not provide sufficient evidence of her relationship, including evidence to show how their relationship started or how their relationship was maintained or developed during periods while her and her partner were living apart," Gilray said.
Malla is currently studying graphic design at the Lebanese University in Beirut.
Garcia said they had photos of their phone calls as evidence on how they kept their long-distance relationship going.
The decision to decline Malla's visa was made by officers in INZ's Beijing office.
"I believe the reason for declining the visa is because we are a same sex couple, and the application was assessed in Beijing, China, a country where... people are being put into camps for being gay," Garcia said.
Same-sex couples are generally frowned upon in China, and until 2001 being gay was regarded as a mental illness.
Garcia said they felt "hopeless and hurt" because there were no avenues for them to appeal the INZ decision.
Gilray said INZ rejects any assertion that it discriminates against individuals who are in a same-sex relationship.
"While a relationship may be a relevant consideration when assessing an application, the fact that it may be a same-sex relationship is not," Gilray said.
"The assessment of a visitor visa requires careful consideration involving the weighing and balancing of all the information provided by an applicant to determine whether they are a bona fide visitor."
These include personal circumstances such as family ties, financial and employment commitments in their country of residence and also their international travel experience, immigration history and purpose of visiting NZ.
"The onus is on the applicant to provide sufficient evidence to demonstrate they meet immigration instructions," Gilray added.
Same-sex couples have been able to marry in New Zealand since 2013, and the country is growing in popularity as a marriage destination for overseas same-sex couples.
There was however no available data on how many overseas lesbian, gay, bisexual, transgender are coming to New Zealand on any visa categories.