If saved money is converted into money designated for trade, does it continue its current hawl (zakat year) or does a new hawl begin, and what about the two months from 6 to 8?

If the shares are for trade, Zakat (definition) is obligatory on them if they reach the nisab (definition) (minimum threshold) and a hawl (full lunar year) has passed over them. The hawl is calculated from the time of owning the original capital used to purchase the shares, not from the time of purchasing them. The questioner delayed Zakat beyond its due time, so he must repent and make up for the Zakat difference between the time it became obligatory and the time he paid it, if his wealth decreased at the time of payment. Zakat is calculated by lunar months, not solar months.