Go to Dirty Muriel's Cornerclub, across the bridge right outside Wolverine Hall. Tenyeminwe is waiting inside, by the door on the first floor. Chat with her about travel together and tell her to come with you; she'll follow you until you instruct her to stop or you reach your destination. Proceed to the docks, on the northwestern side of Sadrith Mora.
The journal message indicating that Tenyeminwe has made it safely to the Elf-Skerring sometimes doesn't show in your journal until you proceed partway down the ramp to the Elf-Skerring. You must receive this journal entry to complete the quest.
If you kill Tenyeminwe, you will be unable to receive any more quests from Skink-in-Tree's-Shade.
Tenyeminwe is not in Muriel's before quest has started and disappears from docks after quest is finished.