Proving cohabitation in Beijing can be a complicated process, but there are a few steps you can take to gather evidence:

1. Conduct surveillance: Hire a private investigator to conduct surveillance on the suspected cohabitation. The investigator can gather evidence by observing the comings and goings of the couple and documenting any evidence of shared living arrangements.

2. Gather documentation: Gather documentation such as utility bills, rental agreements, bank statements, or other documents that show the couple sharing living expenses or financial obligations.

3. Interview neighbors and witnesses: Talk to neighbors or other witnesses who can provide information about the couple's living situation, such as how long they have been living together, how often they are seen together, or if they share any household chores or responsibilities.

4. Take photographs: Take photographs of the couple together at home, entering or leaving the residence, or engaging in activities that suggest they are living together.

5. Obtain a statement from the suspected cohabitant: Try to obtain a statement from the suspected cohabitant confirming that they are living with the other person. This can be difficult, as the suspected cohabitant may not be willing to provide this information voluntarily.

It's important to note that proving cohabitation alone may not be sufficient to establish a common law marriage or other legal rights. You may need to consult with a lawyer to determine the appropriate legal course of action in your specific case.