Since you’re the first holder in both cases, it isn’t considered a “transfer” for capital gain purposes, rather a change in holding pattern. As such, there’s no capital gain.
There’s a reason code, “Transfer between specified family members” which you can consider using.
Please can you advise when these shares are sold in future if the purchase price is the original price or the price as on date when this movement happens from first account to the new account.
Since there are no capital gains at the time of transfer, you should compute capital gains upon selling from the original buy date/price to the price/date of selling.