GST/HST does not factor into any payment unless it is clearly spelled out on the invoice or notice of amount due.

"the business acquired a condo" - is this a business location or residential? what is the purpose of the business owning the condo? What is the line of business for 'the business'. These and more are questions that need to be determined to know the best way to record the expense and whether or not to expect GST/HST to be charged on the management fees.