No, it is not possible.
Either there was a false positive pregnancy test or lab error or there was a miscarriage followed by another pregnancy without an intervening menstrual period. There is no way a pregnancy would stop, then resume growing.
In 1944, hearing the heartbeat for the first time would be done with a stethoscope. There were no doppler devices then. If the heartbeat was not heard until September, then the patient was probably not 4.5 months pregnant any earlier than that date. That would be consistent with the birth in late February. It would be more helpful if the article gave the actual date the heart was heard.
Pregnancy was diagnosed in 1944 using the "rabbit test".
Rabbit test - Wikipedia, the free encyclopedia
A lot of "overdue" pregnancies were due to women missing a period, not actually pregnant, then getting pregnant the first time they ovulated after the cycle with no period. Now, with ultrasound, pregnancies can be accurately dated, thank goodness!