No, they won't be moved automatically.
Edit: That means *existing* linked PDFs. New PDFs downloaded by the Zotero web connector will be moved automatically to the new "move to" folder location.

Edit: If you want to move those existing linked PDFs to the new location ...

You would need to enter the new "move to" folder in Zotmoov, and then repeat the move process to move the linked files from their current location (baked in the Zotero database) to the new location where you want them.

In general, linked file setups are simplest when all linked files are in a single folder. Subdirectories for linked files can get very complicated. If you are trying to match Zotero collections to OS folders, they are also problematic because Zotero collections are not like OS folders - so a 1:1 mapping of PDF locations is not possible.
https://www.zotero.org/support/collections_and_tags#the_zotero_collections_model

With all linked PDFs in a single folder you simply rely on your collection structure in Zotero for organization. Zotmoov should make the displayed file title the same as the file name (not just "PDF"), so it should be easy to find the matching linked PDF in your OS outside Zotero whenever necessary (or by using right-click Show File from within Zotero desktop).

The location move (by Zotmoov) is only automatic for future, new PDFs downloaded by the Zotero web connector. You seemed to be asking about changing your "move to" directory and getting *existing* linked files moved to that different folder. That has to be done manually via Move Selected to Directory. I will clarify that distinction in my original reply.

If you change the "move to" folder later without doing that manual move on existing linked PDFs, you would simply end up with older linked files at the old location (but still locate-able by Zotero, since their location is baked into the database), and future linked files (automatically) stored to the new location. And having different locations for linked files could however create complications over time. For example if you wanted to set up the same linked files on a second computer (making sure they are all copied over from their different locations would be more tedious).

You only really need a Linked Attachment Base Directory (LABD) if your linked files are at different locations on different computers (eg under D:\ on one computer and E:\ on another). The LABD only affects where Zotero *looks* for linked files. It has no effect on where they get stored. People do often confuse the Zotmoov/Zotfile 'move to' folder and the LABD. They may both be set to the same folder, but they do different things.

Since linked files don't work with the mobile apps, the LABD is irrelevant for those. So if you only have one computer, you don't need a LABD. But adding one does not cause any real problems, even if you don't really need it; only that if you later have Zotero on another computer, you will need to remember to add a LABD there too (even if the linked files are in the same location on both computers).

Hi, thank you so much for the discussion. I'm just finding ways to implement this into a workflow where I read/highlight/annotate on PDFs with my iPad Zotero and then manage for Obsidian Zotero Integration with my Mac. Is there a way to do this successfully with ZotMoov? If not, what are my options?

Thank you very much, I managed to solve my problem uploading to the Beta version they recommended to you--not it doesn't crash so thank you very much. :D

EDIT: I just realised this wasn't the discussion thread I thought, sorry! My solution was just paying for the premium version, and with the rate of PDF files I need to manage it's more than worth the money I think. Thank you again!

@Amit3821 firstly, Zotero itself cannot sync linked PDFs to the Zotero mobile apps. That is a fundamental limitation of linked files.
https://www.zotero.org/support/attaching_files#linked_files

So there are only 'workarounds' for mobile access to linked files ...

Firstly, assuming your linked-files folder is mirrored to a cloud service, you should be able to access that folder on your mobile device to open PDFs directly there, in an external PDF reader. Any annotations you add there will be embedded in the PDF. But since Zotero's annotations are not embedded in the PDF (they are stored in the database), you won't be able to see any annotations you had *already* added in the Zotero reader (unless you exported them to the PDF every time, which would be very tedious). However when you get back to your computer, you *will* be able to see any newly-added embedded annotations in the Zotero reader (along with the existing annotations). You can then choose to import those new annotations if you wish (they will remain locked otherwise).

Alternatively, if you want to access linked PDFs in the actual Zotero mobile app, the Zotmoov plugin has options you can set up via its custom menus for that - whereby a linked PDF is *temporarily* moved back under Zotero\storage, from where it will be automatically synced by Zotero to the mobile app in the usual way (as long as you have sufficient online file storage quota; 300mb is free). After working on that PDF in the mobile app, back on your computer you use the reverse Zotmoov menu option to transfer it back into linked storage. Annotations work transparently and seamlessly across those transfers.
https://github.com/wileyyugioh/zotmoov/blob/master/docs/CUSTOM_MENUITEM_INFO.md

Do note that the custom menu example shown in the Zotmoov docs is for a different process - the one that Zotfile supported (Zotmoov's predecessor). That allowed people to access 'stored' PDFs on mobile devices, before the Zotero mobiles apps existed (by temporarily moving them as linked PDFs to a cloud-mirrored folder, accessible on a mobile device; and then extracting embedded annotations to an item note upon their return to local storage).
https://github.com/wileyyugioh/zotmoov/blob/master/docs/CUSTOM_MENUITEM_INFO.md#examples