I have a wired doorbell, but want to keep my existing illuminated wired push button. Can I link my illuminated push button to a Honeywell wireless doorbell?

Yes, Honeywell Home offer a Wired to Wireless Converter (Part number:  DCP917x) that connects to an existing wired Push button and bell transformer which will allow it to work with Honeywell Home wireless doorbells via Honeywell Home ActivLink® or Friedland 868MHz.