Is your coax TV/video coax? If so, be careful with that because the impedance is likely 75ohm and your HT very likely expects 50ohm. How big of a problem that is is up to you to research/decide.
If you don't have appropriate coax some things you could try:
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Adding a tiger tail to the existing antenna (assuming you could reassemble it)
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getting higher up
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If you can't reassemble the OG antenna, use the connector and solder the dipole radiators to it directly