Force Google favicon refresh

I've redesigned a couple of websites and changed their favicons as well. The new favicons shows correctly in all browsers, but in Google mobile search results the old one appear. I have already waited 2 months but it hasn't changed, and I've submitted a sitemap for a re-index. I need a Google SERP expert to help me get my favicon refreshed.

All work needs to be done via remote access and voice call.