I have MSP430F5529 USB LaunchPad and MSP430FG4250IRGZR-16-Bit Ultra-Low-Power MCU. So is there a way to program the mcu using the launchpad.
The Launchpad can program any MSP430 that supports the SBW interface - you can tell these from the datasheet pin descriptions, if the RST pin is described as
/RST/.../SBWTDIO then SBW is supported.
The MSP430FG4250 appears to be one processor in the MSP430 range that doesn't, so ... no.
If you've already made the PCB, you may be lucky enough to find another processor in the MSP430 range that (a) is available in the same package and pin-compatible for the pins you're using , (b) supports the peripherals you need and (c) HAS the SBW interface.
Otherwise it's up to you whether you want to invest in a full JTAG programmer or select a different member of the MSP430 range - this time, checking for SBW.
Table 1-14 of the JTAG programming guide (SLAU320) shows which device families have the SBW interface available.
Of course not! Spy Bi-Wire is a serialised JTAG and cannot be used with the full 4-wire JTAG.
In theory, I suppose that Bi-Wire could be converted to the full JTAG, but it would be a great deal of work, and cost more than simply buying the standard JTAG adapter. They cost $115.