Welcome to a bone of contention and countless arguments and disagreements!!!!!
The official SW literature states 5-15 syns per day. Whether man or woman, 5 stone or 50 stone.
However, some people's consultants say aim for 10 syns a day. Personally, I think that this covers you for if you have underestimated any syns during the day. Again,
personally, I have between 10-15 syns per day.
Other consultants have told people with a lot of weight to lose, that they can have more than the 15 syns per day. (Having seen your stats, neither you or your girlfriend fall into that category).
Actually, forgive me for being nosey, but your bmi isn't that high, so you might find losing weight a bit slow. Your girlfriend's bmi is quite low (officially in the underweight category). I know that bmi is yet ANOTHER bone of contention, but you ought to be aware, that officially SW does not promote itself to those with a low bmi.
BUT.....We are all adults, with our own issues, making our own decisions. So good luck with the plan from sleepy Manchester, UK.
P.S. Sorry for rambling on, and apologies if you think that I've over-stepped the mark.