I'll just mention what happens when you try to move it over, as it simply doesn't work as you'd expect it to work.
Today I've tried to bring accross a Team Site from SharePoint 2013 On-premise to SharePoint Online by using ShareGate Migration. *Almost* everything went well and I decided to do some sanity checks on basic functionalities of the site.
The one thing that's heavily used is a Client List solution that is implemented in the following way:
Page A: A web part page, containing a number of List View webparts, each of them containing different pieces of information related to specific clients, let's say client documents and key contacts.
Client Documents and Key Contacts, for example are separate lists, each of which has an identical column, called "Client" of type "Choice" Each item in those lists is associated with one client only.
Page B: A page with only one list view webpart, visualizing a list called "Clients", with a search box and some groupings which are collapsed so that the whole list of clients is not displayed by default.
The "Clients" lits has a column called "Link", of type guess what (Yes, Hyperlink or Picture of course) which supposed to take you to information for *only* that client on Page A by filtering all webparts on Page A, based on their "Client" column's value - it should be matching the value inserted in "Link". That is achieved through the Query String (URL) Filter webpart.
The format of the link is: http://intranet/sites/teamA/clientlist.aspx?Client=NameofTheClient.
When this is clicked (that's what people do when they find the needed result), they're taken to Page A (clientlist.aspx) and view all info related to the client, with all other clients' data filtered out. Great, isn't it?
So, that was working well on the SharePoint 2013 on-prem, but not in Office 365 as I've tested it now post-migration.
The Query String (URL) Filter webpart is inserted on Page A. It's only visible in Edit Mode and it was visible on the page when I went to edit it. But the functionality that we used to have on premise was not working, when clicking on the "Link" column on Page B, I was taken to Page A, but totally unfiltered and seeing a bunch of data for a number of clients - not what I needed in order to find something quick. And the reason struck me immediately:
It seems the webpart connections are not brought over! I've tried exporting the webpart and importing it manually - still the same thing. The only thing that came over is the "source" of the filter parameter. Let's imagine that one was gone too, so we'd start nice and clean by readding our webpart:
Go to "Add Web Part" and locate the Query String (URL) Filter under the Filters category:
That's how the vanilla version looks like:
Open the tool pane to configure it and choose a meaningful name of your choice for the filter and the parameter that you'll be passing in the query (in our case Client):
On the next screen, choose "Get Filter Values From" and press the "Configure" button:
Choose the target list column that you'd like to use for filtering:
Done. The webpart will now show you the connection(s) rather than the annoying "Unconnected" warning:
Hope that was useful for you if you're tasked with migrating some solutions based on these webparts in your daily work. The interesting outstanding question is where are these connections stored when they're not coming over with the webpart itself? I'll be glad if someone posts a comment with an answer on that mistery.