Firemen had been fighting the forest fire before they could get it under control.

可以呀!下边是两者的区别：
1）can could 表示能力；可能 (过去时用could),
只用于现在式和过去式(could).be able to可以用于各种时态.
They will be able to tell you the news soon.他很快就能告诉你消息了.
2）只用be able to
a.位于助动词后.
b.情态动词后.
c.表示过去某时刻动作时.
d.用于句首表示条件.
e.表示成功地做了某事时,只能用was/were able to,不能用could.
He was able to flee Europe before the war broke out.
= He managed to flee Europe before the war broke out.
注意：could不表示时态
1）提出委婉的请求,（注意在回答中不可用could）.
--- Could I have the television on?
--- Yes,you can./ No,you can't.
2）在否定,疑问句中表示推测或怀疑.
He couldn't be a bad man.
他不大可能是坏人.