FH is a dominantly inherited disease meaning that only one copy of the gene needs to be inherited for someone to show signs of the disease. As we have 2 sets of genes (one set from each parent), someone with FH could have one FH gene and one normal gene for cholesterol. That would give them a 50:50 chance of passing the FH gene on every time they had a child.
In FH, LDL is 4.9 mmol/l or higher whereas your LDL levels fall into the normal range. This would suggest that if your mother did have FH, you were lucky and did not inherit the FH gene from your mother and therefore cannot pass it on to your children. Your GP is right to repeat the test to be sure and, of course, there are other causes of raised cholesterol.