[morzh]

Take the cap off, either by gently pulling (if there is no soldering jojnt anymore, it will just come off) or by desoldering it (melting soder and pulling) . Assumed is that the cap is loose.

Clean the cap by melting solder of and violently shaking it once immediately. The solder will come off exposing the hole.

Scrape and tin the end of the wire. Try to not w9rk close to the glass.
Put the cap back. If the wire does not stick out enough, take the cap and using a blunt speric end (or sharp conical) increase the dent.
Put the cap back again, and flood the protruding end of the wire by solder.

I do not know if there are compounds to hold the cap but, if ot disturbed too much, it will ge ok.