Appeal for entry visa

What's your status in Singapore? Citizen or PR or a foreigner working under a WP? It depends much on the status of your in Singapore. Secondly, you too can explore the opportunity to get marry her in her country. Then, you can apply for her Long term pass but her record in Singapore is hit by her deportation reason. It's not that easy to get a visit visa for a person who caught doing any kind of crime as she caught misusing her visit visa here. Good luck

If ICA does not give her a visa for marrying you here (even on appeal, which I think is probable with her background), then you can only marry her abroad and apply for an LTVP for her afterwards.
You will need sufficient income to feed both of you (for a foreign couple, this means minimum S$6000/month and if you are Singaporean it is a luck thing where an MP might be able to help) - she will probably NOT be allowed to work here again, after abusing a work pass once.
If that doesn‘t work out, you better move to her country or elsewhere together with her. This may sound harsh, but it‘s Singaporean meritocracy in action!
Remark: Things may look more favourable again after you have a child with her and register the baby for Singapore citizenship (not automatic when born abriad!) - preferably a boy, who‘ll be liable for NS (a.k.a. cannon fodder).

Hi i am a Singapore citizen , i am aware of the option to get married overseas. However I am afraid that after doing so she still wont be able to visit SG. That will be a problem in long term. I am thinking of visiting my MP and appeal again. Not sure whether other documents like my gf education cert all these will help?

Hi so if I visit the MP to request for help there might be a slim chance they will write a letter to submit my appeal again?

Singaporeans seem to see a visit to an MP as "cure-all". In my (indirect, as I am not Singaporean and they of course only help people who voted for them) experience, you cannot expect miracles - at most a well-worded letter to ICA, which might or might not change anything (as even after that, ICA will not break regulations or internal orders for you).
If you are applying for a non-working visa (which includes LTVP), educational certificates should not matter. You can still attach those when applying for an LoC (allowing her to work on LTVP) after a year.
Your biggest problem now is dispelling the authorities' assumption that she will work illegally again once back in Singapore. She will not get any visa unless you manage this!

Ya I understand your point the letter is not miracle. So in my position if I were to appeal again is there any suggestion what documents to submit. Previously i only submitted her passport my nric and the MoM letter. I did not submit her previous WP and the letter of appeal written by me might not be very detailed. I am consulting from lawyer/immigration services to draft out my letter. Appreciate much!