Well,
I suggest you to configure both domain in suffix dns on machines. You can user a GPO to configure it, look this exemple.
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In Group Policy Management Editor, expand Computer Configuration, expand Policies, expand Administrative Templates, expand Network, and then click DNS Client.
Right-click DNS Suffix Search List, click All Tasks, and then click Edit.
On the DNS Suffix Search List Properties page, select Enabled. In the DNS Suffixes box, type the primary DNS suffix of the disjoint computer, the DNS domain name, and any additional namespaces for other servers with which Exchange may interoperate, such as monitoring servers or servers for third-party applications. Click OK.
In Group Policy Management, expand Group Policy Objects, and then select the policy that you created in Step 4. On the Scope tab, scope the policy so that it applies to only the computers that are disjoint.
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Related link:
https://docs.microsoft.com/en-us/exchange/configure-the-dns-suffix-search-list-for-a-disjoint-namespace-exchange-2013-help?redirectedfrom=MSDNRegards,
Jaderson Pessoa
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