Yes, you can transfer flotillas to get a VII.
This old list by HammFist shows what uboats are available at what flottilas, when and where the flotillas are based.
1st Flotilla
Wilhemshaven 6/39 to 7/40
Brest 8/40 to 9/44
1939: U-Boat Type IIA
1940: U-Boat Type VIIB
1941: U-Boat Type VIIC
1942: U-Boat Type VIIC
1943: U-Boat Type VIIC
1944: U-Boat Type VIIC
2nd Flotilla
Wilhemshaven 8/39 to 8/40
Lorient 9/40 to 9/44
1940: U-Boat Type VIIB
1941: U-Boat Type IXB
1942: U-Boat Type IXC
1943: U-Boat Type IXC
1944: U-Boat Type IXC
7th Flotilla
Kiel 8/39 to 8/40
St. Nazaire 9/40 to 7/44
Bergen 8/44 to 5/45
1939: U-Boat Type VIIB
1940: U-Boat Type VIIB
1941: U-Boat Type VIIC
1942: U-Boat Type VIIC
1943: U-Boat Type VIIC/41
1944: U-Boat Type VIIC/41
1945: U-Boat Type VIIC/41
10th Flotilla
Lorient 1/41 to 9/44
1942: U-Boat Type IXC
1943: U-Boat Type IXC
1944: U-Boat Type IXC
11th Flotilla
Bergen 1/41 to 5/45
1942: U-Boat Type VIIC
1943: U-Boat Type VIIC/41
1944: U-Boat Type VIIC/41
1945: U-Boat Type VIIC/41
12th Flotilla
Bordeaux 10/42 to 8/44
1942: U-Boat Type IXB
1943: U-Boat Type IXC
1944: U-Boat Type IXC
29th Flotilla
La Spezia 9/41 to 8/43
Toulon 9/43 to 8/44
1941: U-Boat Type VIIB
1942: U-Boat Type VIIB
1943: U-Boat Type VIIC
1944: U-Boat Type VIIC
33rd Flotilla
Flensburg 9/44 to 6/45
1944: U-Boat Type VIIC/41
1945: U-Boat Type VIIC/41
(I have copy pasted this list from
here)