The Original source properties are filled by HubSpot Analytics tools based on the URL's contact's come from and whatever cookied information may be available. This resource will describe circumstances under which original source may be populated as 'Offline Sources' and speaks directly to the use cases you describe.
It should also be noted that the cookie information available at the time of conversion can have a HUGE impact on the resulting Original source property in HubSpot. One example would be of a visitor who HubSpot can identify as having originally arrived on your HubSpot tracked page from a Google search result. If that visitor is cookied by HubSpot in Jan (likely), then converts from that same cookied device on a HubSpot contact form after having clicked one of your LinkedIn posts in Feb, their original source will show 'Organic search' -- not 'Social media' (as one might expect)!
Finally, we have the option of changing the original source value in HubSpot when appropriate. However, we'd recommend weilding that power with extreme caution -- see change original source value. (important)
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