I just Googled it, and this is what I found [1]:

When a country's currency appreciates in relation to foreign currencies, foreign goods become cheaper in the domestic market and there is overall downward pressure on domestic prices. In contrast, the prices of domestic goods paid by foreigners go up, which tends to decrease foreign demand for domestic products.

A depreciation of the home currency has the opposite effects.

It contradicts directly your claim that exports don't get cheaper. You're saying exports remain the same (because they don't get any cheaper), and that the only change is an increase of corporate profits at the expense of wages.

[1] https://en.wikipedia.org/wiki/Currency_appreciation_and_depr...