CRA states that a Holdco which takes over its wound-up subsidiary's business cannot use the sub’s GST/HST registration number
If a GST/HST-registered subsidiary carrying on a taxable business is wound-up into its parent, the parent must apply for a new registration number (using its own business number) rather than taking over the sub’s registration number. The Regulations pursuant to ETA s. 272 deem the parent to be a successor of the subsidiary for small supplier exemption purposes, so that if the sub was not a small supplier, the parent likely will not be one either.
Neal Armstrong. Summary of 23 March 2017 CBA Commodity Taxes Roundtable, Q.10 under ETA s. 272.