I have installed the Hubspot-Salesforce integration where all contact properties are of two-way sync. The setting to sync lifecycle stage between the deals and associated contact/company is turned on as well.
However, when I did a test where I updated a deal stage to Closed Won, the associated contact's lifecycle stage did update to Customer in HubSpot, but this didn't sync over to Salesforce. The associated contact's lifecycle stage remains unchanged in Salesforce.
I tried clearing cache data and tried logging into Salesforce on incognito tab but it didn't work either.
Anyone knows why the lifecycle stage didn't sync over to SF?
I want to share with you this documentation. Did you create a custom field in Salesforce for that? If you did, I would recommend connecting with HubSpot Technical Support, as Support is included in your subscription and they will be able to provide real-time assistance for this matter, where you are able to share screenshots and specific examples about this.