Hi,
I understand your concern.
Mini pill has to be taken at a fixed time ,to get perfect
contraception.In case a pill is missed, it should be taken as soon as realized, & the routine dose should be continued as per schedule. It is advised to use additional care ( condom) for following two days of missing the pill.
In case your your partner has followed above said precaution, there is no risk of conception.
But if she has not resumed the routine schedule after replacing the pill- there is some risk of
pregnancy.- as even precum has few active sperms.
To rule out pregnancy, blood
HCG test around expected date of menses can be useful.
In case it's +ve, get fully investigated for placement of the embryo- & follow the specific advise given by the doctor.
Thanks.