I found his mothers brother which may be a match to the uncle Frank mentioned when immigrating.
Per/Peter Pettersson, b. 5 APR 1855 in Södra Finnskoga, Värmlands län, Värmland.
Emigrated 30 MAY 1883 from Kyrkbyn no 9, Undersvik, Värlmlands län, Värmland.
What do you think, could that be the uncle?