No. You can not share a folder inside of another shared folder. This means, you want to share a link to the parent folder of the shared subfolder. If you try to do this, the recipients will get the link access to all folders in that path. So any changes they make to files in that folder won't sync with your Dropbox. If you give them read-write access to the parent folder, you can unshare the subfolder, share the parent folder and then share a link to the subfolder.
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