How do two non motile gametes fuse to form zygote without mobility?

Your friend is right.

Male gamete reaches the female gamete through pollinating agents like wind, insects, birds, water for fertilization.  For example: Plants which are pollinated by winds contain light and non-sticky pollens which can be easily carried by winds to the stigma of the other flower or other plant. When the pollen grains fall on the stigma, the pollen tube enters one of the synergids and releases two male gametes. One of the male gametes fuses with the egg to form the zygote.