She had submitted Work and Income review forms in 2012 and 2013, in which she falsely stated she was single and did not have a partner, and as a result, continued to receive the benefit.
When she was interviewed regarding this in November 2013, she said they did not live together all the time.
The majority of the payments related to the domestic purposes benefit, now called sole parent support, but also included accommodation supplements.
Judge Barbara Morris remanded Albrett-Rimene at large to reappear in court for sentencing on June 9.
The maximum penalty is seven years' imprisonment.
Sole parent support is a weekly payment given to a single parent or caregiver with one or more dependent children aged under 14 years.
A person applying must be one of the following:
-Living apart from their partner and lost the support or being inadequately maintained by the spouse or partner.
-Divorced or had their civil union dissolved.
-Single.
-Has lost support of their partner as their partner has been imprisoned or is subject to release or detention conditions that prevent employment or, their spouse or partner has died.