I have a fiance our marriage is fixed. but no official dates are announced. it may take more one year. she does not have father and is working in same company where I work. for now can we do mutah for a period of a week or a day. because of our sexual urges we do not want to do haram but we thought it would be halaal if we do mutah. and after doing mutah can I do permanent marriage to her after a year? can I have sexual intercorse in mutah. as we don't want to discuss this with both of us parents . mine or her. she does ñot have father he expired, she has mother and sister. how do I do mutah. what is the process. can I do mutah in this month before arbayeen?

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Your fiancé has to take permission from her guardian. As you mentioned that her father has passed away( may Allah grant him place in Jannah)
Now her mother is guardian her permission is must.
Yes after the muhtaj you can do the permanent marriage. But for example if you are doing Muta for 15 months and if month or days left before your permanent marriage then in this situation you have to gift her the remaining period then you can do permanent marriage.
As per the shariah it is not Haram before arbaeen. But only few days left if in respect of aza if you wait for few days it will be better.