The scan report does not indicate any abnormality in the foetal position. Normally the foetus presents in the head low position only. It is good position. At 39 weeks, the foetus does not change the position. The scan has not mentioned anything abnormal about foetal position - even the deflexion or extension of the head also. So let me presume that the head is flexed.
Doctor has given you 1st June as cut off time for the sake of foetal maturity probably. He/she does not want the baby to become over mature which then may become too big to be accommodated in the mother's passage and also may face some risk during uterine contractions.
The scan does not mention any untoward findings. There is good possibility of normal
vaginal delivery.
The valuable suggestions are:
1. Ask her just to relax
2. Report to the hospital when she
i. starts getting increasing uterine pains with blood stained mucoid
vaginal discharge.
ii. Gets watery vaginal discharge
iii. Any vaginal bleeding
iv. Movements of the baby diminish
Wish your wife an uneventful vaginal delivery and happy parenthood to both of you.