Ask Mr. Smarty Plants

Callicarpa americana (American beautyberry) is considered hardy from USDA Hardiness Zones 7 to 10. Medina, OH is in Zones 5b to 6a, average annual minimal temperature -15 to -5 deg. F. On that alone, we would not believe it very likely that the shrub, which is native to North Carolina,  would survive in your area. 

However, it won't cost you anything to experiment. Here are the Propagation Instructions for the American Beautyberry:

Propagation Material: Seeds
Description: Seed, Root cuttings, softwood tip cuttings and to a much lesser extent division of mature clumps

We were unsuccessful in finding any indication if the berry should be planted directly into the soil or dried, cleaned and refrigerated first. So, if you have berries left, we would suggest you just sow them where you think they might grow, just as if they had dropped off a shrub as winter began. You could also sow them in pots with potting soil. Here are their Growing Conditions so you will have a good idea of where is the best place to put the seeds.

Water Use: Low
Light Requirement: Part Shade
Soil Moisture: Moist
CaCO3 Tolerance: Medium
Cold Tolerant: yes
Heat Tolerant: yes
Soil Description: Moist, rich soils, Sandy, Sandy Loam, Medium Loam, Clay Loam, Clay, Acid-based, Calcareous 

Since you obviously don't have mature clumps to divide, that only leaves taking cuttings. Whether your branch is still viable, we couldn't say, but you will need to take those cuttings right away, if you want to try that. Here is our favorite website on propagation by cuttings, from North Carolina State University Horticulture Information Leaflet, Plant Propagation by Stem Cuttings. 

From our Native Plant Image Gallery:

Callicarpa americana

Callicarpa americana

Callicarpa americana

Callicarpa americana