Step 1: Understand what decides if a drug crosses the placenta.
Large, highly charged molecules cross the placenta poorly, while small, less charged, fat soluble molecules pass through easily. This single idea explains why heparin and warfarin behave so differently in pregnancy.
Step 2: Check unfractionated heparin.
Unfractionated heparin is a large, strongly negatively charged molecule. Because of its size and charge it cannot cross the placental barrier, so it is considered safe for the fetus and is a preferred anticoagulant in pregnancy. This statement is correct.
Step 3: Check low molecular weight heparin.
Low molecular weight heparin is smaller than unfractionated heparin but it is still a large, charged molecule that does not cross the placenta in any meaningful amount. Saying that it can cross the placenta is wrong, and this is the false statement the question is looking for.
Step 4: Check warfarin.
Warfarin is a small, fat soluble molecule that crosses the placenta freely. This is exactly why it is avoided in pregnancy, since it can cause warfarin embryopathy and fetal bleeding. This statement is correct.
Step 5: Check breastfeeding on warfarin.
Warfarin binds very strongly to plasma proteins in the mother's blood, so almost none of it passes into breast milk. Breastfeeding is therefore considered safe for the infant even when the mother is on warfarin. This statement is correct.
Step 6: Final answer.
The statement that is NOT correct is that low molecular weight heparins can cross the placenta.
\[ \boxed{\text{Low molecular weight Heparins can cross the placenta}} \]