If you do not have the resources to synchronize the bitcoin blockchain, your other option would be to dump your private keys from Bitcoin GUI (Bitcoin QT) and then sweep or import them into an SPV wallet like Electrum.
In your Bitcoin QT client open up the debug window and navigate to the console and follow the instuctions below:
Before you do any of these, go to your source directory of your Bitcoin blockchain and backup everything. Backup your wallet.dat file (this is very important) and keep this safe.
Type these in your console:
1) walletpassphrase your-wallet-passphrase 300 (What this does is it'll decrypt your wallet if you have a passcode set for 300 seconds)
2) dumpprivkey <your bitcoin address> (This will give you the private key for the address on which you're receiving funds)
Important: NEVER reveal this private key to anyone else, or else you'll risk losing your funds.
Now download electrum from
https://electrum.org/ (Verify the signatures, you'll find guides to do it on the forum)
1) Open up electrum and select Auto-connect to server.
2) Click standard wallet
3) Click use public or private keys
4) Paste your private keys and it'll create a master spending wallet
Note: Your electrum wallet here will not have a seed, and I highly recommend you to make a seed based wallet later by sending your funds from your current electrum wallet to another wallet which is seed based.
Now once you do this you'll see your fund in electrum, but make sure you always create a Seed based wallet in electrum as this one is safest and easier to note down on a piece of paper and to restore at a later time rather than having to note down your private key.
There's also a very detaild and safe guide over here for paranoid users if you need to do it:
https://en.bitcoin.it/wiki/Safely_Transfer_Bitcoin_from_a_wallet.dat_File_to_Anywhere,_Using_Air-Gapped_Offline_System,_Bitcoin_Core,_and_ElectrumHope this has helped.