Can you please advise whether there are any standard terms of trade as you have indicated there was no agreement.
I assume that the professional services firm, would at the very least have standard terms of trade, which would normally specify that the Courts of Victoria have exclusive jurisdiction, and that the laws of Victoria apply.
If there is nothing agreed with regard to jurisdiction, or applicable laws, then the claim can be lodged in the NSW (the state of the Defendant)... or depending on how the cause of action has arisen... the value and nature of the claim.. it could be lodged in the the relevant small claims tribunal (VCAT or NCAT).. the Victorian Courts or the Federal Courts.
MAGISTRATES' COURT ACT 1989 (VIC) - SECT 100
Extent of jurisdiction
(1) The Court has jurisdiction, subject to subsection (2)—
(a) to hear and determine any cause of action for damages or a debt or a liquidated demand if the amount claimed is within the jurisdictional limit; and
(b) to hear and determine any claim for equitable relief if the value of the relief sought is within the jurisdictional limit; and
(4) The Court does not cease to have jurisdiction in respect of a cause of action because—
(a) part of the cause of action arose outside Victoria—if a material part of it arose in Victoria; or
(b) the whole cause of action arose outside Victoria—if the defendant resided within Victoria at the time of being served with the complaint.
I would highly recommend a Deed of Settlement be prepared by your lawyer and signed by all parties prior to any moneys being paid. This will ensure that the payment is in full and final settlement of the matter.
What you are suggesting with offering a cheque with the words "In Full and Final Settlement..." with the acceptance being evidenced by the banking of the cheque... might be possible, (I would need to conduct legal research to be able to advise further) however... in these matters it is best that nothing be left to doubt... therefore, a Deed of Settlement is highly recommended.
Please advise if you would like me to send you a quote for legal service to prepare the Deed of Settlement.