Hi Roger,
The Narvik naval battles are very difficult to research, as there are a lot if incorrect information (on both sides). In most British files they state that no vessel were afloat in Narvik after the second battle 13.4, but this is not correct according to the reports given by civilian German and Swedish sailors in their reports to their companies and in official hearings. The loss of the Aachen (and the Lippe) is in detail described in a report to the NDL by one of the first officers.
Here is an extract:
9.4.40: First officer Evers of the Aachen takes command over the British prize Mersington Court.
10.4.40: The Aachen is abandoned by the crew due to her dangerous position, and the crew assist in rescuing survivors from German destroyers. In addition to some German vessels, the Cate B., Saphir, Blythmoor and Romanby (there exist other information about her loss) were sunk. After the fighting the crew of the Aachen re-embarked her, and used her cranes to remove guns and ammunition from the British steamers.
11.4.40:
The Aachen unloads AA guns (ex British) at Fagernes, and spend the night at the damaged quay.
12.4.40: Finishing the unloading, again anchoring in the harbour. No damages on the Aachen from the British air attack the same afternoon.
In the evening most of the crew are ordered ashore to seek cover from further attacks.
13.4.40: The remaining crew abandon the Aachen during the fighting, and most of them withdraw to Beisfjord. In the fighting the Lippe is severely damaged, while the Aachen still is operational, but damaged (hull and engine working)
15.4.40: The civilian crews are ordered to return to Narvik to conduct military duty. Lippe and Aachen are prepared to be scuttled as block ships (Hafensperre) by their crews.
16.4.40: Most of the crew from the Aachen works ashore with unloading the Jan Wellem, while the remaining crew moves her to Framnes, where she is to be scuttled. They do not succeed to moor the Aachen in wanted position, and she is abandoned in the evening. All useful equipment and provision are taken ashore.
20.4.40: The crews are ordered home in the evening, and leaves Narvik the next day trough Sweden.
Due to this the Aachen was still afloat 16.4, and most probably sunk no later than 20.4. (ref earlier writing from Dorgeist and myself). Due to the wreck's position, the Germans didn't manage to moor her as a block ship. The wreck was easy lifted in 1951 and prepared to be repaired as Norwegian Oakhill (owner: Holmen & Vabon, Kristiansand - LAKP) During the southbound towage, the rope broke, and she drifted ashore 1.12.51 and sank (still on the seabed). She was bound for Kristiansand, and further to Bremerhaven for repairs.

Hopes this gives some more details :-)
Best regards
Erling