Can you give the exact dates?
The judgement against your ex husband awarded fees to the solicitor.
It is therefore not your obligation to pay. They need to chase down the exH.
(Also, fwiw, their bill should be itemised, with dates, length of call, number called, letter date. )
But that's all moot. The important point is that since the court ordered hour H to pay costs they have to go after him for their money.
The court will have a record of that judgement. You can get a copy if you need one. The sol firm should have a copy too in your file, which should have stayed in the firm even if the sol left.
Take a look at your own copy of the order if you have it. Make sure it says what you believe it says. Send the sol firm a copy and query the fact that the bill was sent to you. Do not send the original in your possession.
Say nothing more than
'I am in receipt of your bill of (date).
I enclose a copy of ( court order, dated x/y, 20??). A copy should be in your files too.
Best regards ...