One method is to use **Python** and copy the values, symbol colour and label from the categorisation of the line layer to the point layer. We can store the line symbology attributes in a dictionary and create a new style using the stored values.

You can test the following code, changing the names of the layers and the field name:

    from PyQt4.QtGui import QColor
	style_dict = {}
	layer_1 = QgsMapLayerRegistry.instance().mapLayersByName("Line example")[0]
	renderer = layer_1.rendererV2()
	if renderer.type() == "categorizedSymbol":
		for cat in renderer.categories():
			style_dict[cat.value()] = (cat.symbol().color(), cat.label())

	categories = []
	layer_2 = QgsMapLayerRegistry.instance().mapLayersByName("Point example")[0]
	for classes, (color, label) in style_dict.items():
		symbol = QgsSymbolV2.defaultSymbol(layer_2.geometryType())
		symbol.setColor(QColor(color))
		category = QgsRendererCategoryV2(classes, symbol, label)
		categories.append(category)

	field = 'ID'
	renderer = QgsCategorizedSymbolRendererV2(field, categories)
	layer_2.setRendererV2(renderer)
	layer_2.triggerRepaint()

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Example:

[![Example][1]][1]

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**Edit:**

If you want to also copy the same field name used in the line layer, replace:

    field = 'ID'

with:

    field = renderer.classAttribute()


  [1]: https://i.sstatic.net/aAzMl.png