To share your report with the client/colleague you need to copy the link from the tool:
Report that will be accessible by this link will include all updates in metrics. Thus, data about new posts, engagement changes, etc. will be reflected in the report automatically.
However, please note that in case if you make any changes in the report design inside Report Builder, the link changes. That means that any time you edit your report by adding new comments or including/excluding sections, a new report with a new link is built. Old link will contain old comments and sections configurations.
If you make any changes outside the Report Builder (add/delete influencers to/from the campaign, change their prices, etc.), these changes will be reflected in ALL versions of your report (by all links that were generated).