袖の振り合わせも他生の縁
ふでのふりあわせもたしょうのえん
even accidentally touching sleeves with a passing stranger is caused by fate
袖ふりあうも他生の縁 is read as そでふりあうもたしょうのえん (sodefuriaumotashou no en) and means even a chance meeting can lead to a deep bond.
そでふりあうもたしょうのえん
sodefuriaumotashou no en
ふでのふりあわせもたしょうのえん
even accidentally touching sleeves with a passing stranger is caused by fate