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As you don‘t seem to be interested in solving the problem, I‘ll stop supporting here.
Just for other readers: 1607 does not get any updates beyond 2018-04, which explains, why no 2018-05 update gets detected. I can‘t find out, what exactly is missing on the machine, so anything further would be speculation.

Topic closed & account banned for 7d

Small addendum: 1607 RS1 14393 will not get any updates beyond 2018-04 for the CB and CBB branch, the "normal" Windows 10 RS1. The Windows 10 Enterprise LTSB2016 is also RS1 and will get further updates! The same is true for Server 2016 RS1.

Still supported:
- LTSB2015/LTSC2015 (TH1 10240)
- LTSB2016/LTSC2016 (RS1 14393)
- Server 2016 LTSB/LTSC (RS1 14393)
- 1703 all
- 1709 all
- 1803 all