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The opposite however, is not true. Money can not be transformed in time. If it could, old billionaires would spend it to buy extra years for their lives.

I don't think this statement is true. Anyone who saves up money & spends it on a vacation has bought time - free time, at least, and presumably it's time being spent on something they'd rather be doing than working.

Also, when we spend money on any labor-saving device we're exchanging money for time. IOW, we spent time to make money, which we used to buy a labor-saving device which saves us time. So we spent time to make time, with a conversion into money and a second conversion out of money in the middle. In that case I think it does work both ways.

What you say is true. You can paint your own kitchen, but you can also pay someone to do it for you. In that case you have bought/saved time with your money.

However, in the case of "Time heals all wounds" this is not the case. You cannot pay someone else to do your grieving, and you can't buy a machine to do it for you. You just have to 'sit it out', and this sort of time can't be bought.