Let's see if I made a mistake. First, assume we're trading on the North American side of the Atlantic.
Buy 10 shares of Arcam at $20 a share when the exchange rate is, say, 2 SEK = $1, meaning (and so far this has been approximately true), that in Sweden they would be selling for 40 SEK a share.
Assume the SEK drops to an exchange rate of 4 SEK = $1 and that Arcam is still selling for 40 SEK a share there. Moreover, assume Arcam is at status quo, in other words, there's no news that changes their perceived future value. On our market 40 SEK a share in Sweden means we should be seeing in the neighborhood of $10 a share here.
So, as the SEK drops in value relative to the dollar, the share price of Arcam drops. In this case 1 SEK was at first worth $0.50 and dropped to 1 SEK being worth $0.25. That's the direct relation of which I speak.
