Hi Nelly -
You might try "partner" and "statement" in your search, etc.
Here is an excerpt from our client info sheet on suggestions for partner visa applicant/sponsor statement content - hope it helps!
Statements Written by the Australian Sponsor and Visa Applicant
Your own statements should detail the history of your relationship and explain how you both have a commitment to a shared life together, that your relationship is genuine and continuing and how you intend to live together.
Below is a list of topics and areas you may wish to use to guide your writing:
• How you met, when you met, and where you met
• The types of things you tended to do together during dating and courtship (including places you went out, things you did together, etc)
• How the relationship progressed and became stronger/closer
• Details of shared financial and other responsibilities.
• Details of how you organise your household finances.
• Details of family and social events with friends and relatives
• Details of holidays taken together or weekends away, etc.
• Details of how one partner is supportive of the other partner’s lifestyle choices, social activities, sporting and recreational activities, friends and family.
• Details of how you intend to live together.
• Details of your commitment to each other. Please also comment upon any intent you may have to marry in the future (if prospective marriage applicant), raise a family (if applicable) and any other specific plans or goals for your life together in the future