Does the consulate general sign life certificates?

Yes, the consulate general is authorized to sign and stamp life certificates. 

The applicant must visit the consulate in person and bring a valid photo ID, preferablly a passport or a HKID. Life certificates are signed during office hours, weekdays at 9-12. No appointment needed. 

For more information please visit the Swedish Pensions Agency's (Pensionsmyndighetens) webpage