Let me make this clear, sharing the S/N to obtain a Recovery Image that is not intended for your device is against the EULA of Windows:
https://www.microsoft.com/en-us/Useterms/OEM/Windows/10/UseTerms_OEM_Windows_10_English.htm Specifically -
Restrictions. The manufacturer or installer and Microsoft reserve all rights (such as rights under intellectual property laws) not expressly granted in this agreement. For example, this license does not give you any right to, and you may not:
(i) use or virtualize features of the software separately;
(ii) publish, copy (other than the permitted backup copy), rent, lease, or lend the software;
(iii) transfer the software (except as permitted by this agreement);
(iv) work around any technical restrictions or limitations in the software;
(v) use the software as server software, for commercial hosting, make the software available for simultaneous use by multiple users over a network, install the software on a server and allow users to access it remotely, or install the software on a device for use only by remote users;
(vi) reverse engineer, decompile, or disassemble the software, or attempt to do so, except and only to the extent that the foregoing restriction is permitted by applicable law or by licensing terms governing the use of open-source components that may be included with the software; and
(vii) when using Internet-based features you may not use those features in any way that could interfere with anyone else’s use of them, or to try to gain access to or use any service, data, account, or network, in an unauthorized manner.
And -
Downgrade Rights. If you acquired a device from a manufacturer or installer with a Professional version of Windows preinstalled on it, you may use either a Windows 8.1 Pro or Windows 7 Professional version, but only for so long as Microsoft provides support for that earlier version as set forth in (aka.ms/windowslifecycle). This agreement applies to your use of the earlier versions. If the earlier version includes different components, any terms for those components in the agreement that comes with the earlier version apply to your use of such components.
Neither the manufacturer or installer, nor Microsoft, is obligated to supply earlier versions to you. You must obtain the earlier version separately, for which you may be charged a fee. At any time, you may replace an earlier version with the version you originally acquired.