I have a user who sent an email last night from outlook (2013 SP1 fully patched), on their desktop computer at work to another co-worker who sits in an office in same building but it was not received until this morning.  Looking through the headers of the email I can see that it did not enter Exchange (Exchange 2013 Cu7) until this morning when it was promptly delivered less than a second later.

Does this rule out an issue with Exchange or are there logs I can look at within Exchange to see why it took so long for the email to make it into Exchange?  I'm sure this email was stuck in his outbox but could an issue within Exchange cause emails to stay in the outbox?  If the issue was within Exchange wouldnt I see the delay in the header?  Just need some advice on where to start looking into this.  Thanks

The email headers will show the timestamp of the message when it was handled by each mail server, very likely this will include your correspondent's SMTP server .

In users sent item, what is time status of the sent items there?

Have you checked Queue Viewer on Your Exchange server to see if you have many mails stuck there?

yes, all exchange queues look fine but but if the delay was because of a message stuck in exchange queue would that not be reflected in the header as a delay between the servers?

the time stamp of the item in sent items in the senders outlook is last night at 7:03pm but his colleauge did not get the email until 5:35 am this mroning.  But the headers show the email did not make it into Exhange until 5:35am and was delivered within a second later.

yes, all exchange queues look fine but but if the delay was because of a message stuck in exchange queue would that not be reflected in the header as a delay between the servers?

the time stamp of the item in sent items in the senders outlook is last night at 7:03pm but his colleauge did not get the email until 5:35 am this mroning.  But the headers show the email did not make it into Exhange until 5:35am and was delivered within a second later.

Do you use Cached Mode or Online mode?  If cached mode, there is a chance he shut the machine down or lost connectivity before Outlook was able to pass the message on to the transport service, so when he booted it up this morning Outlook was able to connect to Exchange and pass the message to the transport service, who processed the message.

yes first thing I asked if he was in cached mode which he is but he I looked through event logs and could find no evidence that the machine was shutdown at all or that any network connectivity was lost, he leaves his machine on at all times and outlook is always running

What about sleep mode? 

the user wouldnt be able to send the email if the computer was in sleep mode