1939 Roo Halfpenny

What are the reasons for your doubts?

I don't think these are scarce enough for the fakers to bother with, even if I have seen much more common coins faked.
From the pictures, looks OK to me.
Looks like slight impact damage next to the 'G' of 'GEORGIVS'.
Rim denticles look a bit odd below 'PENNY'.

You can try the usual tests to begin with:
1.) ring test
2.) weigh it
3.) Check the edges, (not shown in pictures)

Looks like a bit of an off centre strike.
The rim at the top is thinner than at the botom.
Thats why the denticals look wierd.
Or could be squashed at the bottom.
If not EF+
I doubt that our asian mates to the north would bother with these
Ef+
Nice coin

The ring test is easy.
Just rest the coin on the tip of a finger, and tap the rim with the rim of another coin. Compare the tone of the ring with a known genuine coin.

I rest the coin I want to test on one finger, and a known genuine coin to test it against, on an adjacent finger. Takes a little to develop the skill, but it is easier to compare one ring immediately after the other. I usually do this test whist sitting on the edge of a bed, so that the coins do not accidentally drop on a hard surface.

Sel, I gave the ring test a go and it sounded just like 3 other half pennies I have. Thanks for info I had not thought to do this before.

silver has its own tone as well when struck. the older coins have a higher note then the newer lesser silver in them coins, a bit like crystal the note holds for a few seconds as well