Very fine hair 2 months after beard transplant. Will it thicken?

You cannot expect "density" after two months. Your results will not likely show for another 6 to 12 months.

2 months is too early to judge the result of  a hair transplant.  A small group of patients may start growing hair from the begging, but most patients lose all transplanted hair and nothing grows until month 2-3. Initially all hairs are short and fine but they will thicken up over time and 6-10 months are better time to judge your final look.

At this time because the grafts usually shed, you can not tell what it will look like until the grafts grow out at about 8 months when 80% of the hair will be there and growing