Which other wallet could act as a server?

[NotAPonzi]

Is it possible for multibit, electrum or armory wallets to run like a server like the bitcoin core wallet would run using the -server command? I am tired of waiting on the bitcoin core wallet blockchain to download. I will be connecting the wallet to a php script hosted on a website

[Welsh]

Creating a Bitcoin client that fully implements the network protocol is extremely difficult. Bitcoin-Qt is the only known safe implementation of a full node. Some other projects attempt to compete, but it is not recommended to use such software for anything serious. (Lightweight clients like Electrum and MultiBit are OK.)

You can download the Bitcoin bootstrap torrent to speed up the process of syncing. The torrent will speed up the process, however it won't complete instantly.

Who wants bootstrap.dat?

Anyone bringing up a new node using the reference client.  This is one method of accelerating the initial blockchain download process, while helping the bitcoin P2P network by offloading data download traffic from public P2P nodes.

This download is not for those who are already running the bitcoin client.

[shorena]

Is it possible for multibit, electrum or armory wallets to run like a server like the bitcoin core wallet would run using the -server command? I am tired of waiting on the bitcoin core wallet blockchain to download. I will be connecting the wallet to a php script hosted on a website

If you are talking about the initial sync use the torrent like Welsh suggests or the new 0.10.0rc3 version of bitcoin core. It supports headers first and can download from multiple nodes at once, which makes the sync faster.

If you are talking about the daily sync because you shut the machine down, think about running a node without wallet on a server and use e.g. mSIGNA.