1) Jack is a couple years older than Hen, and took his examination early himself. This is a bit tricky, since they're supposed to be very close in age and served together very early on.
2) Hen was posted to another station (West Indies? North America?) at the time he would have otherwise taken his examination and had to wait until he returned to Europe. If I remember correctly, at the point that Jack and Hen were taking the examination, you needed to go to the Admiralty itself, though this changed.
Any other ideas? I'm really in the middle of packing my house for moving (and may be delayed in responding) so I haven't the leisure to look other things up in my Muster Book (though for anyone else who has it, there is an entry on Jack's service prior to April 1800).
(the fact I can actually spell Lieutenant right without looking it up amuses me. I can't spell at all.)